### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Note for MATH 1431 with Professor Balthazar at UH final exam review

### View Full Document

## 18

## 0

## Popular in Course

## Popular in Department

This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 18 views.

## Reviews for Note for MATH 1431 with Professor Balthazar at UH final exam review

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

1 Find the following limits if they exist sin 7x a 11m xrgt0 9x b lim 5x gt0 tan2x x3 8 c 11m 2 xrgt2 x 4 2 d lim x 1 gt1 x1 6 lim 511101 hgt0 h f 1 In1 005k mo h 1 limi g xgt1 x 1 h 1 1 00 2x xgt0 x Ax Z xgt 1 Math 143 1 Final Exam Review 3x lim gt0 s1n4x 2x cot3x x1 11ml gt1x 3x2 x2 3x2 11m gt4 x2 1 1im3x2 2x 1 XHZ 2 We know that lim2x 1 3 Give the largest value of 6 that works with 8 2 1100 in the proof of this KHZ limit 3 Use the de nition ofthe derivative to compute the derivative of fx Vx 1 4 Find values ofA andor B so that the function is continuous x2 x lt 1 Ax B x 1 a fxA 3 gt1 b fx 3x 1ltxS2 x x sz A x gt 2 3x2 1 x lt 4 c A x 4 Bx 1 x gt 4 5 Determine ifit is possible to find A so that fX is continuous and ifit is find A Ax x gt 3 x2 1 x lt 3 a x b 8 x 3 f x23 x33 fx Ax 1 x gt 3 2 x 2 xlt 1 2x1 x32 C fx 1 x d fx Ax2 3x xgt2 6 Find the derivative of the following a fx x3 2x b y 0053 2x c fx x tan x d fx 3x cos2x 2xZ x2 3x e fx f f x sinx2 2x x x22 g fx h y cosx2 3x5 i fx sin2x cos3x3 j fx 4sin x cos5x5 k fx sin2x 1 fx cos3x m fx tan4x n fx c0tx 0 fx secx p fx csc2x q fx 2x3 4x2 7 r fx xsinx s fx m t fx 1x1 u fx tan 2x x4 7 Use the intermediate value theorem to show that the function fx 2x5 3x 1 has a root on the interval 7 1 2 2x2 7 3x 1 8 Use the extreme value theorem to show that the function fx has both a maximum and a A minimum value on the interval L 1 2 9 Notice that le 12 is asolution to the equation xy3 y 10x Compute dydx at m 12 10 Give an equation forthe tangent lineto the graph ofthe function fx 2x2 7 3x 1 atthe pointwhere Xl 1 1 Suppose we are given the data in the table ahoutthe functions fand g and their derivatives Find the following values x 1 z 3 4 ffx 3 2 1 4 f39fx 1 4 2 3 gx 2 1 4 3 339le 4 2 3 1 0 M4 If hrfgr 17 4 If hrfgr 5 M4 If hgt6 fgtlt 01 4 If hgt6 fgtlt 2 4 If hI f 4 If hrfrgr 12 Each ofthe graphs below are graphs off Determine where f is increasing decreasing intervals of concave up and concave down c 1 3 The value m2 is a critical number nr x Classin 1 as a Inca maximum Inca minimum m neither a fxx312xzx0 12x2 x 15 Give the differential ui fx 3 at x 1 with raspactlntha increment 110 15 Use the guess x 3 and une itaratinn ui Newlnn39s mathndtn apprnximate a rant ui fx 17 Use differentials to approximate V63 18 Evaluate a 114 3dt dx 3 d 2 b 3t 4 t dx H d 2x21 C 1 1m dx3xt x25x d 1 dt dx 3 ZI wf e Disint2dt d 273 d7 0 sinl 2 dt x 19 The function fX given below is continuous find a formula for fX a 2x4 3x2 6 J39ftdt 2 b 2x3 3x2 x 1Jftdt 71 20 Integrate a csc2 x dx I Vcotx b Ixsz x c 3 2x2 5dx d j dx 1 1 l x dx ED gab f Isin3 3x cos 3x dx 7 g va x2 de cos 3xdx sec2 2xdx csc2 3xdx 0 J sec2xtan2xdx p I mdx q I xx2 14 dx 21 Give the average value of fx x2 on the interval 02 22 Given the graph at x With the area at regirnA tr equal tr 73 regirn E is 343 and regirn c is 73 Find a The area rithe regirnhruneeehy x andlhexraxis between V2 and 4 h fxdx 2 23 Use the de nitinn Di derivative a find the derivative Di a fx3xzrx2 h fx 7h 3xrl 2 4 Given Fx irr each prrhlern graph the lunctirn and shade the area between x and the xraxis line the x7 errreinate at the eentrrie at the shaded regirn and line the yrcnnrdinate at the eentrrie at the shaded regirn a Fx 2 h Fx x2 Me 25 Given Fx anethe interval a h graph x ever the interval rinethe average value at Fx rnthat interval and line the value at cthatveri esthe ernelusirn at the rnean valuetherrern er integrals irrthe unclinnaner the interval a b a Fx x2 e x 01 in Fxx23x 730 c F0 4 722 26 Write the equatinn nithe tangent line a a y exy60attheprint52 E u eSxyery 4 atthepnint 31 27 28 29 30 31 32 33 34 35 36 37 As a balloon in the shape ofa sphere is being blown up the volume is increasing at a rate of4 in3sec At what rate is the radius increasing when r 1 in Sand is falling offa conveyor onto a conical pile at a rate of 15 cubic feet per minute The diameter of the base ofthe cone is twice the altitude At what rate is the height of the pile changing when itis 10 feet high You have a square piece of cardboard 6 inches wide and 16 inches long that you wish to fold into a box It occurs to you that you can cut an equal square from each corner ofthe cardboard make a crease along each side and fold the sides up to make the box How much should you cut from the corners to form the box with maximum volume A man is walking away from a light pole at a rate of 5 feet per second If the light pole is 20 feet tall and the man is 6 feet tall how fastis his shadow growing when the man is 30 feet from the light pole A rectangle is drawn in the first quadrant so that its base is on the x axis and its left side is on the y axis What is the maximum area of this rectangle ifits upper right vertex lies on the line segment connecting the points 40 and 08 Suppose f is a differentiable function on the interval ab a Explain how to find the absolute maximum and absolute minimum values of f on the interval ab b Use a graph to demonstrate that a function can have its absolute maximum value occur at exactly 3 places Consider the function fx 3x4 20x3 42x2 36x on the interval 04 a Show that the critical numbers of f are 1 and 3 b Give the intervals ofincrease and decrease of f c Give the values ofX at whichf has either a local minimum or a local maximum d Give the values of X at which f has an absolute minimum or an absolute maximum e Give the interval 5 where the graph of f is concave up f Give the intervals where the graph offis concave down g Give the values of X where the graph of f has inflection h Plot f State the extreme value theorem State the mean value theorem Give a geometric explanation of Newton39s method Graph a functionfwhich has a cusp at x 1 a vertical tangent line atx 2 a horizontal asymptote of 3 and vertical asymptotes atx 2 and x 3 38 List the domain critical numbers intervals ofincrease intervals of decrease in ection points intervals of concave up and intervals of concave down for the function given Then graph the function and carefully label any local maximums local minimums or points ofinflection 3 fxx12x2 1 9 b x x4 2x2 f 4 4 c fx 2x3 3x2 12x 3 39 R is the region bounded by the given graphs and the given axis Sketch each graph then find the area of R the volume when R is revolved about the XaXis and the volume when R is revolved about the yaXis a yx2y6 x x cvcis b yx2y6 x y cvcis 40 Let fx x3 3x be defined on 1 1 Find 0 on 1 1 that satisfies the conclusion ofthe Mean Value Theorem 41 Use two iterations of Newton39s Method to estimate the solution to fx 0 for fx x3 x 3 starting at x1 1 42 Estimate tan28 using differentials 43 Find the net area bounded by the graph of fx x3 x2 and the X aXis on the interval 02 44 Find the area bounded by the graph of fx x3 x2 and the X aXis on the interval 02 45 Find the centroid ofthe region bounded by the line y 4 and the graph of fx x2 46 Revolve the region in problem 45 about the xaxis and give the integral resulting from using the method ofwashers to find its volume Do not compute the integral 47 Revolve the region in problem 45 about the yaXis and give the integral resulting from using the method of cylindrical shells to find its volume Do not compute the integral 4 48 Derive the formula V E 39r3 for the volume ofa sphere ofradius rby revolving the region bounded by a circle of radius r centered at the origin around either the XaXis or they axis 49 Compute the Riemann sum for the function 2x on the interval 02 associated with the partition P012 given that the heights ofthe rectangles are created by using the midpoint of each subinterval V1 39 2 1 50 Give the definite integral associated with the Riemann sum Z ilj i n 11 11

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.