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Calculus 1

by: Rae Kutch

Calculus 1 MATH 155

Rae Kutch
GPA 3.8


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Class Notes
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This 16 page Class Notes was uploaded by Rae Kutch on Saturday September 12, 2015. The Class Notes belongs to MATH 155 at West Virginia University taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/202661/math-155-west-virginia-university in Mathematics (M) at West Virginia University.

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Date Created: 09/12/15
Math 155 7 Spring 2002 REVIEW WORKSHEET 11 NAMF x Section 1 For the function at 2 310 on the interval 0 1 do the following a Write the Riemann Sum for the partition of 01 into the 4 subintervals 0 i E g g 2 1 When the left hand endpoints are selected for the b Use the regular partition of 01 into 71 equal subintervals and select the right hand endpoints for the to write a Riemann Sum for c Compute the value of the Riemann Sum in part b for n 5 2 Consider the sum 71 39 i 1 31 211 sin n n a Explain Why the sum can be interpreted as a Riemann sum for a function at on the interval 01 That is guess the function at the partition and the selection Math 155 7 Spring 2002 REVIEW WORKSHEET 8 NAMF x Section 1 For the functions below do the following i Determine the critical points ii Determine the open intervals Where the function is increasing and Where it is decreasing iii Classify the critical points a fx37271 b 910 Saul5 7 x65 c 2sec2ac on 77r47r4 64 is d W ms 36 2 An open topped rectangular box is to have a volume of 1441113 If its bottom is rectangular With a length 3 times its Width find the dimensions of the box that Will maximize surface area Math 155 7 Spring 2002 REVIEW WORKSHEET 10 NAMF x Section 1 Evaluate the following inde nite integrals a W3i5dx b 5374de c 4 7 25 dt d 4 sec22x 7 5 sec3x tan3ac dac d 1 2 Find a solution of the initial value problem i dye 90 12 3 The following inde nite integrals require more thought to find the antiderivatives a 2x dac V3ac2 b 3V1 cost32 dt c l sec6l3 tan6l sec6 d6 Math 155 7 Spring 2002 REVIEW WORKSHEET 3 NAMF x Section 1 Apply the limit laws and the theorems of Section 24 to show that the function 33374 279 1 is continuous on x gt 3 2 Determine Where the function 1 ac 7 2ac 3 is continuous Explain your reason ing 3 Discuss the existence of the left and right hand limits at x 71 for the function 7 70163 ifxgil flti250 ifxgt7l for a fixed contant c ls it possible to choose the value of c so that the resulting function is continuous at x 71 How and explain 4 Find the limit hm me h 7 my hgt0 h When f4x and gt74 5 Can the function at W be rede ned to be continuous at the point x 5 Explain you answer 6 Explain Why the equation 32 l 5 510 has a solution in the interval 0 l Math 155 7 Spring 2002 REVIEW WORKSHEET 9 NAMF x Section 1 Given the equation 2 y2 7 cos7rxy 14 do the following a Use implicit differentiation to find Ty or 2 at b Verify that the point P1 12 satis es the equation Since the equation de nes y implicitly as a function of at y at With f1 12 write the equation of the tangent line to the graph of f at the point P1 12 2 Find the second derivative of the function gt sin2t 543 DO NOT SIM PLIFY x 2 3 Let at Please carefully sketch the graph of y In so doing an 7 please identify and label the open intervals of increasing and decreasing the local extrema the open intervals of concave up and down and the horizontal or vertical asymptotes Math 155 7 Spring 2002 REVIEW WORKSHEET 13 NAMF x Section 1 Find the area between the two curves y 2 7 9 and y 310 7 9 2 Find the area bounded between y 13 and y 3 for at between 0 and 1 3 Find the area of the region bounded by the three curves y 2 y 7220 8 and y ac 7 22 7 4 for at between 0 and 4 Math 155 7 Spring 2002 REVIEW WORKSHEET 6 NAMF x Section 1 Find the speci ed derivatives DO NOT SlMPLlFY a find far for at 12 sec3ac 1 15 cost3 sint l b find gt for gt c find hQ for Mel tan46sec26 csc l2 d find fO for at xtanac sin3 A straight Wire 60 inches long is bent by a right angle into the shape of an L What is the length of the tWO legs of the L so that the triangle formed by adding a third side has maximal area N 1 3 Find the shortest possible distance from the point P0 l to the parabola y E152 74 4 Find the critical points and the absolute extrema for the function at x2 7 3023 on the interval 03 Math 155 7 Spring 2002 REVIEW WORKSHEET 14 NAMF x Section 1 Consider the region bounded between the two curves y 2x4 and y 2 l a Find the volume of the solid found by revolving the area around the xv axis b Find the volume of the solid found by revolving the area around the line at 71 2 Find the length of the curve y ac 7 132 When x is from 1 to 6


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