# UH MATH 1431 - ch 1 and ch 2 test review (10 pages)

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## ch 1 and ch 2 test review

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- Pages:
- 10
- School:
- University of Houston
- Course:
- Math 1431 - Calculus I

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Math 1431 Exam 2 Review Material Covered Chapters 1 and 2 Know your instructor s name Know your lab s TA name lab s time and room number Test 50 minutes CASA Testing reservation required Test is part multiple choice and part free response with parts You will have the multiple choice grade right away but the free response will take some time to grade No formulas are provided No calculators allowed You will be given scratch paper For the free response you ll be given stapled pages asking for your name lab info etc to do all your free response work on Show all your work here and not on the scratch paper Do the practice test 20 attempts allowed for more practice and extra credit 1 Evaluate the following limits if they exist 5 a lim x 2 x 1 x 0 x 2 b lim x 2 x 1 x3 x Math 1413 Test 2 Review 1 2 c lim x 3x 10 x 2 x 2 4 4 x 2 d lim x 0 x 2 Find the following limits if they exist sin ax a and Recall lim x 0 bx b lim x 0 1 cos ax 0 bx sec 5 x x 0 2x a lim b lim x 0 5x tan 9 x Math 1413 Test 2 Review 2 1 cos2 2 x x 0 7x c lim d lim 1 cos 2 x x 0 sin 6 x 3 The function f is given below along with its graph Find the following limits if they exist 2 x 7 x 2 f x x 2 1 2 x 2 x 1 2 x a lim x 2 f x b lim x 2 What type of discontinuity occurs at x 2 Math 1413 Test 2 Review f x c lim f x x 2 at x 2 3 4 Find the points of discontinuity if any Classify each as removable jump or infinite a f x x3 4 x 2 x 1 b f x x3 8 x2 2 x a 3 b3 a b a 2 ab b 2 a 3 b3 a b a 2 ab b 2 5 Determine if the following function is continuous at x 2 If the function is not continuous state the type of discontinuity x 2 5 x f x 7 x 2 x 2 5 x 2 Step 1 Is f 2 defined Step 2 Check to see if lim f x exist lim f x must equal lim f x x 2 x 2 x 2 Does lim f x exist x 2 Step 3 Does lim f x f 2 x 2 Hence f x is Type i e Compare 1 and 2 above CONTINUOUS at x 2 or DISCONTINUOUS at x 2 JUMP REMOVABLE INFINITE Math 1413 Test 2 Review 4 6 Find the values of a and b such that f x is differentiable ax 2 10 x 2 f x x 2 6 x b x 2 You must first check continuity at x 2 f 2 lim f x x 2 lim f x x 2 Next work on differentiability f f Math 1413 Test 2 Review 5 7 Find the derivative of the following functions using the definition f x h f x Recall lim h 0 h f x x2 5x 8 Find the derivative of the following 1 a f x sec x tan x 2 2x Math 1413 Test 2 Review 6 b f x 3 3 x 1 2 c f x 4 x x2 x 3 d f x x 1 x 1 x 2 Math 1413 Test 2 Review 7 e f x sin 4 4 x 2 6 x 1 9 Find d3 dx 3 10 Find 11 Find dy dx 3 4 3 x 2 x x 10 4 x 2 for f x x 2 cos 2 x dy using implicit differentiation for x2 y 2 xy 7 dx Math 1413 Test 2 Review 8 12 Find the equation of the tangent line to the curve f x x at x 0 1 tan x 13 Write the equation of the normal line to sin x cos y 0 at the point 4 4 Math 1413 Test 2 Review 9 14 Suppose we are given the data in the table about the functions f and g and their derivatives Find h 2 if h x f x g x 2 x 1 2 3 4 f x 3 2 1 4 f x 1 4 2 3 g x 2 1 4 3 g x 4 2 3 1 Extra Review Questions for Lab Find the derivative of the following functions using the definition f x h f x Recall lim h 0 h 2 a f x b g x x 2 x 4 Math 1413 Test 2 Review 10

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