01/02/14

Find h'(1)?
Let f and g be differentiable functions such that f(1)=2, g(1)=2, f'(1)=3, g'(1)=-3, f'(2)=-4, g'(2)=5. If h(x)=f(g(x)), find h'(1).   Answer: 12
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01/02/14

Find the integral?
If ∫ f(x-c) dx from 1 to 2=5 where c is a constant, find ∫ f(x) dx from 1-c to 2-c.   Answer: 5    
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01/01/14

Which of the following?
Which of the following is true about the graph of y=ln abs(x^2-1) in the interval (-1, 1)?   a) It is increasing. b) It attains a relative minimum at (0, 0). c) It has a range of all real... more
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01/01/14

For which of the following choices?
Let f(x)=3x+1 for all real x and let ε>0. For which of the following choices of δ is abs(f(x)-7)<ε whenever abs(x-2)<δ?   a) ε/4 b) ε/2 c) ε/(ε+1) d) (ε+1)/ε e) 3ε   Answer: A
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12/31/13

Find the number?
  The number of bacteria in a culture is growing at a rate of 3,000e^(2t/5) per unit of time t. At t=0, the number of bacteria present was 7,500. Find the number present at t=5. Answer: 7,500e^2
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12/31/13

Find a series?
Find a series expansion of sin(t)/t.   Answer: 1-t^2/3!+t^4/5!-t^6/7!+...   Do I must memorize the formula for Maclaurin Series for problems like these?
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12/30/13

Find the value?
  Let y=x*sqrt(1+x^2). When x=0 and dx=2, find the value of dy. Answer: 2
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12/29/13

For what non-negative value?
For what non-negative value of b is the line given by y=-1/3x+b normal to the curve y=x^3?   Answer: 4/3    
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12/29/13

Find the set of values?
If f(x)=x+1/x, find the set of values for which f increases.   Answer: (-∞, -1]U[1, ∞)   I know that f'(x)=1-1/x^2=0 and x=1, -1. But what to do next?
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12/29/13

What's f(1)?
If f"(x)-f'(x)-2f(x)=0, f'(0)=-2, and f(0)=2, what's f(1)?   Answer: 2e^-1    
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12/28/13

Is a number between?
If f(x)=8-x^2 for -2≤x≤2, f(x)=x^2 elsewhere, then ∫ f(x) dx from -1 to 3 is a number between?   a) 0 and 8 b) 8 and 16 c) 16 and 24 d) 24 and 32 e) 32 and 40   Answer: D
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12/28/13

What's f(x)?
If ∫ x^2*cos x dx=f(x)-∫ 2x sin x dx, what's f(x)?   Answer: x^2*sin x+C    
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12/28/13

If n is a non-negative integer?
If n is a non-negative integer, then ∫ x^n dx from 0 to 1=∫ (1-x)^n dx from 0 to 1 for?   a) no n b) n even, only c) n odd, only d) nonzero n, only e) all n   Answer: E    
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12/27/13

What's f'(1)?
If f(x)=(x^2+1)^(2-3x), what's f'(1)?   f'(x)=-3*ln(x^2+1)*(x^2+1)^(2-3x) f'(1)=-3*ln(2)*2^(-1)   But the answer is (-1/2)*ln(8e)    
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12/27/13

Find the largest delta?
Find the largest delta that could be used successfully with an arbitrary e in an epsilon-delta proof of limit of (1-3x)=-5 as x approaches to 2?   Answer: delta=e/4    
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12/26/13

Find an equation?
Find an equation of a curve that intersects at right angles every curve of the family y=1/x+k (where k takes all real values)?   Answer: y=(1/3)x^3    
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12/25/13

For what function?
∑ ((-1)^n*x^n)/n! is the Taylor series about zero for what function?   Answer: e^-x    
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12/24/13

What's f(x)?
If the graph of y=f(x) contains the point (0, 2), dy/dx=-x/(ye^x^2) and f(x)>0 for all x, what's f(x)?   I integrated and got c=2. But I have trouble for finding y. Please show all the... more
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12/22/13

The region bounded by the x-axis?
The region bounded by the x-axis and the part of the graph of y=cos x between x=-pi/2 and x=pi/2 is separated into two regions by the line x=k. If the area of the region for -pi/2≤x≤k is three... more
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12/22/13

The point on the curve?
The point on the curve x^2+2y=0 that is nearest the point (0, -1/2) occurs where y is?   Answer: 0
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12/21/13

The area of the closed region?
  The area of the closed region bounded by the polar graph of r=sqrt(3+cos theta) is given by what integral? Answer: ∫ (3+cos theta) dθ from 0 to pi How can you find this?
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12/21/13

What's h'(x)?
If h(x)=f^2 (x)-g^2 (x), f'(x)=-g(x), and g'(x)=f(x), what's h'(x)?   Answer: -4f(x)g(x)    
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12/21/13

What's the limit?
What's the limit of (8(1/2+h)^8-8(1/2)^8)/h as h approaches to 0?   Answer: 1/2
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12/19/13

What's the closest integer approximation?
Let R be the region enclosed by the graph of y=sin e^x^2, the x-axis, and the lines x=-1 and x=1. What's the closest integer approximation of the area of R?   Answer: 2   Since it's x-axis,... more
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12/18/13

What are the asymptotes?
What are the asymptotes of the graph of the parametric equations x=1/t, y=t/(t+1)?   Answer: x=-1, y=0.
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