Review Sheet with Practice Exams - Calculus I | LB 118, Exams of Calculus

Download Review Sheet with Practice Exams - Calculus I | LB 118 and more Exams Calculus in PDF only on Docsity! LBS 118 – EXAM # 2 - REVIEW SHEET with PRACTICE EXAMS. Your actual exam questions may vary slightly from these, but will cover the same topics. You are expected to know how to use ALL of the derivative rules we have covered in class… The only formulas I will give you will be the derivatives of the ARCTRIG (INVERSE TRIG) functions. 1. Find the EQUATION of the tangent line to the curve 2 29 4 3 0x y x y+ − + = at the point (4,0) 2. Find the derivatives: (DO NOT SIMPLIFY the answers.) a) 4sin 3tanx x y x − = b) 2 2cot( 2) csc( 2)y arc x arc x= − + − c) 12csc(3 ) arcsin(3 )y x x= d) 2ln( 2 3)y x x= − + e) 24 cos 2 1xy e x= + + − f) 52 log x y x= + 3. Use logarithmic differentiation to find the SLOPE of the curve at x = 2: ( )2 3 2 3 2 ( 1) x x y x − − = − 4. Find 2 2 d y dx for the curve 23 7x y− = . Simplify and give your answer in terms of x & y only. 5. A penny is dropped from a 300 ft building with an initial velocity of –20 ft/sec. Note: 2 0 0( ) 16s t t v t s= − + + . a. Find the POSITION and VELOCITY of the coin after t = 3 sec. b. Find the TIME it takes for the coin to reach the ground. c. Find the VELOCITY of the coin at the moment it hits. 6. A particle is moving back and forth along the x-axis. Its position is given by the equation: 3 29 15 10s t t t= − + + , where s is in feet and t is in seconds. a. Find the VELOCITY and ACCELERATION functions. b. When is the particle stopped? Moving backward? Moving forward? c. When is it moving at a constant speed? Slowing down? Speeding up? d. What is the total distance traveled over the first 10 seconds? 7. Sand is falling into a conical pile at a rate of 15 ft3/min. The DIAMETER of the cone’s base is approximately twice its height. At what rate is the height changing when the pile is 10 ft high? 8. Tell where the following function is differentiable. Give a reason for your answer: 1 3( ) ( 2)F x x= − 9. Tell where the following function is differentiable. Give reasons for your answers. Remember: Differentiable leads to continuous, but continuous does not lead to differentiable. REVIEW the TRUE/FALSE QUESTIONS from the text and make sure you understand them well enough, so that if I change them slightly you will still be able to answer them! MORE PRACTICE EXAMS FOLLOW… LBS 118 EXAM #2 NAME: Practice Exam. Find the DERIVATIVES of the following functions. DO NOT SIMPLIFY YOUR ANSWERS. Make sure to include parentheses wherever needed. An answer from a calculator is not good enough. 1. ( ) ( ) 1 2 5 2 32 3y x x x= − − 2. 2cot(3 ) 5 cot(3 ) csc (3 )y x acr x x= − + [ ] 2: cot 1 d u NOTE arc u dx u ′− = + 3. 2 2 2 1 x y x   =   +  4. 4 ln(2 3)xy e x= − 5. Find the EQUATION of the tangent line to 3 8 6y y x+ = − at the point where y=1. 6. Use logarithmic differentiation to find the slope of the curve at x=1: ( ) 33 7 2 3 x x y x + − = + 7. A ball is thrown vertically upward with initial velocity of 80 ft/sec. Its height is given by the function 2( ) 80 16s t t t= − . a) HOW LONG does it take the ball to hit the ground? b) What is the VELOCITY of the ball when it hits the ground? 8. A 15 ft ladder is leaning against the wall of a house. The top of the ladder is sliding down the house at a rate of 2 ft/sec. How fast is the base of the ladder moving away from the house when the top of the ladder is 2 ft from the ground? (A decimal answer is OK. Make sure to LABEL the units of measure for your answer.) 9. The graph of f(x) is given here. State at which x-values the function is NOT differentialbe. Give reasons for your answers. Answer the following questions TRUE or FALSE. If the answer is FALSE, give a REASON or COUNTEREXAMPLE. 10. If a function is NOT DIFFERENTIABLE at a point, then it is CONTINUOUS there. 11. If a function is CONTINUOUS everywhere, then it is DIFFERENTIABLE everywhere. 12. 1 3( ) ( 2)f x x= − is DIFFERENTIABLE everywhere.