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# Study Sheet for Exam 1 210

SUNY Oswego

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## Popular in Calculus I

## Popular in Mathematics (M)

This 9 page Study Guide was uploaded by Nadelyn Pichardo on Monday September 14, 2015. The Study Guide belongs to 210 at State University of New York at Oswego taught by Patrick R Halpin (P) in Fall 2015. Since its upload, it has received 24 views. For similar materials see Calculus I in Mathematics (M) at State University of New York at Oswego.

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Date Created: 09/14/15

1 Find the domain of the function fix 2xx1 fx 2x1ifoS1 2 Graph the function 1x2ifxgt1 3 3 Express the function F x 2 x I as the composition of three functions figihixm Identify f g and h x f2h f2 x1 evaluate the difference quotient h and simplify your 4 If x answer 5 Using a complete sentences state the definition of a function 6 Let flx4x2 Where x30 a Sketch the graph b Determine the domain and range of fx c Find the equation of f1 State the domain and range of f1 1 d Sketch the graph of f on the set axes in part a be sure to label each graph properly 5 3 a a a 7 The function f xi x 95 95 1s one to one Determ1ne the followmg a f 13 f b Haul 12 8 Express as a single logarithm 1 xy1nxyzmz 9 Solve the equation log2X4 2 10 Find the exact value of a arccos7 sin3 rI 2 b 6 1 111 6 l l 11 A The point P 11 is on the curve 3 2 if Q is the point X Z use your calculator to find the slope of the secant line PQ correct to six decimal places for the following values of X 11 101 1001 10001 B Using the results from part A guess the value of the slope of the tangent line at X 1 x3 1 1 Use your calculator to sketch the graph of f in a Window 12 Let x x x3 1 containing x 1 Then from the graph determine g x1 13 Use limit laws to determine each of the following limits hm a39 x gt4 x2 3x 4 lim x2 b39 x gt5 X 53 x29 5 C 11m xgt 4 X4 14 An object is thrown directly upward with an initial velocity of 64 ft s Its height in feet 2 above the ground t seconds later is given by y 64t16t Find its average velocity during each time period below 111 1 101 1 1001 1 10001 b Write a sentence that explains how the object s instantaneous velocity at t1 second may be determined using part A above Determine the instantaneous velocity at t1 second 15 3 a The point P 2 8 is on the graph is f x x Corresponding to each value 3 of X below the point Qix x is a point near P on the graph For each X determine the slope of the secant line passing through P and Q Round slopes to five decimal places x221 x2201 xZZIMI xL9 x2199 xl999 b Write a sentence that explains how the slope of the line tangent to 3 f x x Ax 2 may be determined using part a above and then determine the slope of the tangent line c Write the equation of this tangent line 16 State the Intermediate Value Theorem 17 Use the Intermediate Value Theorem to show that there is a root of the equation H x Smx 1 0 on the interval 0 3 Your explanation should be clear and complete 18 Determine if each statement is true or false 39 39 If 12 x 2 and 8x 0 then gx does not exist 39 39 fx b If Ef x 0 and 128p 0 then 12 gx does not exist

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