Calculus Midterm Questions

Use geometric properties to evaluate S(top 7 bottom 2) Ix-4Idx

13/2

Use the Trapezoidal Rule to estimate the definite integral [Use n=4] S(7 on top 3 on bottom) (x^2 + 10x +1)dx

310

differentiate: y= arcsin(5x)

5/(1-5x^2)^1/2

Use a Riemann sum to approximate the area under the curve, and above the x-axis, for the curve y= e^x from x=0 to x=4. Use 4 sub-intervals and midpoints

51.428

let ye^x - x= y^2 find y'

solve for dy/dx answer= (1-ye^x)/(e^x -2y)

Find the equation of the tangent line to the graph of x^2 + 2y^2 = 3 at the point (1,1).

y-1 = -1/2(x-1)

If f(x)=sin(2x)cosx, then F'(Pi/3) =

-5/4

If f(x)=x^2e^x find a point where the tangent is horizontal

(-2, 4/e^2)

S lnx/2x dx =

(lnx)^2/4 + c

Given f(x)= Ax^3 + Bx^2 +cx + D and 1. f(1)= -1, 2. f'(1)= 10, f"(0)= -4, f"(1)= 14. What is the value of (A+B+C+D)?

-1

The point (6,2) lies on the graph of f(x)= (x-4)/(x-5). Find the slope of a line tangent to the graph at that point.

-1

Determine S(1+1/x)x^-2dx

-1/x -1/2x^2 +c

If y=6sin x/3, then d^2y/dx^2 =

-2/3sin x/3

Given f(2)= 3, f'(2)=4, g(2)= -2, g'(2)= -4. Find h'(2) if h(x)= f(x) x g(x).

-20

S dx/25+x^2 =

1/5 tan^-1(x/5)+c

d/dx S (x^3 on top and 5 on bottom) (dt)/(t-7) =

answer= (3x^2)/(x^3-7)

Find the absolute maximum value of F(x)= x^3-3x^2-9x on the closed interval [0,6]

54

Use p Properties of integrals to find S(top b bottom a) (f(x) +4)dx, if S(top b bottom a) f(x)= 5A-3B.

A+B

Find instantaneous rate of change of the function F(x)= x^3 + 5x^2 - 3

Just find the derivative answer= 3x^2 +10x

If y= e^ln(cosx), what is dy/dx

The e and the ln cancel out then you find the derivative of cosx answer= -sinx

Find a number C in the interval [1,4] that satisfies the hypothesis of the Mean Value Theorem, if f(x)= (x^2 + 4)/x

do (f(4)-f(1))/3 you get 2

what is the slope of the tangent line to x^2y + xy^2 =12 at the point (1,3)

find derivative and then plug in (1,3), solve for dy/dx for the answer answer= -15/7

differentiate s(t) = sec t^1/2

find the derivative answer= (sec t^1/2 * tan t^1/2)/(2* t^1/2)

Given f(x)= 2^3x, find f'(0)

ln 8

a sly fox starts at t=0 and moves along a path that can be related to the x-axis so that its postion at any time t> or = 0 is x(t)= t^3-6x^2+9x+12. During what time interval is the fox moving to the left?

plug in numbers to find if they are positive or negative, If positive move to the right, if negative move to the left. answer= 1<x<3

Let f be defined as the following: f(x)=( x^2+5 for x>5) and (3ax for x< or = 5) for what value of a is the function continuous?

set the equations equal to each other and plug in 5 , then solve for a a=2