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OldMathTest#2-1 - d Simplify your answer using the product...

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Old Test #2 from another section of Math 141 No Calculators. Show all work. 1. From the following graph of the derivative, dx dy , (I’ll put on the board) a. On what intervals is y increasing? b. At what values of x are the maxima of y? c. Is y concave up at x=3? d. Answer Why? To part c. 2. Find the derivative of the following functions: a. 6 ) sin ( ) ( x x x f = b. )) ln(arctan( ) ( x x g = c. x e x x k + = 2 ) ( 3. ) ( ) ( ) ( t b t a t w = with w(0)=1, b(0) = 7, a’(0)=2, b’(0) = 8. Find w’(0). 4. This step-by-step process will be similar to our shortcut derivations in class: a. Write the limit definition of the derivative for a function g(x). b. Let g(x)=cosx. Substitute this function into the definition of the derivative from part a. c. Use cos(a+b) = cosa cosb – sina sinb
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Unformatted text preview: d. Simplify your answer using the product and sum laws of limits. e. Use 1 ) sin ( lim = → t t t and ) 1 cos ( lim =-→ t t t to show the final steps. 5. Just a short answer (and a short time) should be fine for the following: a. Calculate the 401 st derivative of y = sinx. b. At what values of t is ) 1 )( 3 ( 1 ) ( +-= t t t g not differentiable? c. Calculate the derivative of θ sec ) ( = m using that the secant function is the reciprocal of cosine function. 6. Given 2 3 400 7 tan x y y = + , find dx dy . 7. Use logarithmic differentiation to find the derivative of 5 7 2 4 x e e x y x x + = ....
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