Unit 3
Find f'(x) if f(x) = cos-1(-7x), simplify
f'(x) = -1/√(1-49x2)
Using the first derivative test, find the interval on which the function, f(x) = -2x2+4x+3 is increasing
(-∞,1)
Evaluate
∫-12 6x(x2-1)2dx
27
The function s(t) is a baby's shoe size at time t, which of the following differential equations describes linear growth in the baby's shoe size?
(A) ds/dt = 2s
(B) ds/dt = s2
(C) ds/dt = 2
(D) ds/dt = 2t
(E) ds/dt = t2
(C)
nth Term can determine divergence for which of the following?
I. Σ∞n=1 sin(2n)
II. Σ∞n=1 (2 + (3/n))
III. Σ∞n=1 (n3+1)/(n2)
(A) II only
(B) II and III only
(C) I and II only
(D) I, II, and III
(D)
Find f'(x) if f(x) = arcsec(x3), simplify
f'(x) = 3/|x|√(x6-1)
Use the second derivative test to find the x-value at which there is a point of inflection on the function
f(x) = x3 -6x2 +12x
x=2
Approximate the value of the integral
∫13 x3-3dx with four sub-intervals and right endpoints, simplify
Find the general solution of the differential equation dy/dx = x2/y .
y= +/- √(((2x3)/3) + C)
Which of the following is a divergent p-series?
A. Σ∞n=1 (1/4)n
B. Σ∞n=1 n(-1/2)
C. Σ∞n=1 n(-3/2)
D. Σ∞n=1 n(3/2)
B.
Use the chain rule to find the derivative of
f(x) = (6x2+7x)4
f'(x) = 4(6x2+7x)3(12x+7)
Find the absolute max of the function
f(x) = 2x2+3x2+4 on the interval [-2,1]
Absolute Max = 9
Evaluate ∫-30 -8x/(2x2+3)2 dx, simplify
4/7
Let h(x) = ∫1x √(1+t2) dt . Use Euler's Method, starting at x=1 with 2 steps of equal size to approximate h(3).
√2 + √5
Find a bound for R20 when approximating Σ∞n=1 (-1)n+1/n by S20
1/21 or 0.0476
Find d4y/dx4 if f(x) = 7sin(x/3) + cos(1-2x)
f(4)(x) = 7/81sin(x/3) + 16cos(1-2x)
Find the C value that satisfies MVT on the interval [-2,1] when f(x) = -x2/2 +x -1/2
C = -1/2
Evaluate ∫4/(x2+5x-14) dx
-4/9ln|x+7| + 4/9ln|x-2| + C
or
4/9ln|(x-2)/(x+7)| + C
Which of the following is/are solution(s) to the differential equation y'' - 5y' + 4y = 0
I. y = 5cos(2x)
II. y = 2ex
III. y = Ce4x , where C is a constant
I & III
Let f be the function defined by f(x) = e2x . Find the first 4 non-zero terms for f', the derivative of f?
2 + 4x + 4x2 + (8x3)/3 + ... + (2(2x)n)/n! + ...
Find the slope of the tangent line to the graph of x2y+y4=4+2x at the point (-1,1), simplify
4/5
Using the second derivative test, find the interval on which the function, f(x) = x(x-4)3 is concave down
(2,4)
Use integration by parts to find
∫0𝜋 x2cos(4x)dx, simplify
(1/8)𝜋
Consider the differential equation dy/dx = (y-4)3 sin(πx/2) . There is a horizontal line defined by the equation y = C , that satisfies dy/dx . Find the value of C .
C = 4
The third Maclaurin polynomial for sin 𝑥 is given by 𝑓 = x - x3/3! . If this polynomial is used to approximate sin(0.3), what is the LaGrange error bound?
|(sin(0.3)/24) * (0.3)4|