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CALC PONY PG 2

# CALC PONY PG 2 - a Write one sentence explaining why f(x...

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1. Consider the function f(x) = 4x + 1 defined for any real value of x. a. Write one sentence explaining why '(x) has an inverse function. b. Draw the graph of the inverse function. -2 x . . 2 c. Construct a formula for the inverse function. Answer: , - 1 ( X) = 2. Using the definition of derivative, not any derived formulas, find the derivative of f (x) = 1-+ 1 . (SHOW x . ALL WORK) 3. Consider two functions p(x) and v(x) both of which are exponential. The initial value of p(x) is 25 and the decay rate is .03.The initial value of v(x) is 31 and the decay rate is .04. Use the natural log to find the value of x for which p(x) = v(x). (SHOW ALL WORK) 4. The stopping distance.fora ship under its own drag is proportional to the square of its speed. A large tanker traveling at 10 knots requires 15 miles to stop. Find the stopping distance at 3 knots. (SHOW ALL WORK) 5. Simplify the following'expressions. Stopping Distance = a. sin(arcsin(2k+ 1)) a) Answer: sin(arcsin (2k + 1)) = b. e 3hl( x) b) Answer: e31n(X) =

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1. Consider the function f(x) = 4x + 1 defined for any real value of x.
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Unformatted text preview: a. Write one sentence explaining why f(x) has an inverse function. b. Draw the graph of the inverse function.-2 x . . 2 c. Construct a formula for the inverse function. Answer: f - 1( X) = 2. Using the definition of derivative, not any derived formulas, find the derivative of f (x) = ~ + 1 . (SHOW . x . ALL WORK) 3. Consider two functions p(x) and v(x) both of which are exponential. The initial value of p(x) is 25 and the decay rate is .03. The initial value of v(x) is 31 and the decay rate is .04. Use the natural log to find the value of x for which p(x) = v(x). (SHOW ALL WORK) 4. The stopping distance for a ship under its own drag is proportional to the square of its speed. A large tanker traveling at 10 knots requires 15 miles to stop. Find the stopping distance at 3 knots. (SHOW ALL WORK) 5. Simplify the following'expressions. Stopping Distance = a. sin(arcsin(2k + 1» a) Answer: sin(arcsin (2k + 1» = b. e 3 hl( x) b) Answer: e3ln(X) =...
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CALC PONY PG 2 - a Write one sentence explaining why f(x...

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