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Calculus
The Great Courses Study Workbook for... Understanding Calculus: Problems, Solutions, and Tips
430 SOLVED PROBLEMS
Question: 2.P.3
Test the equation y = x² / x²+1 for symmetry with respect to each axis and the origin . ...
Verified Answer:
It is symmetric with respect to the y-axis, becaus...
Question: 2.P.2
Find the intercepts of the graph of the equation x√16 – x² . ...
Verified Answer:
y-intercept:
y=0{\sqrt{16-0^{2}}}=0;(0,0).[...
Question: 2.P.1
Sketch the graph of the equation y = 4 – x² by point plotting. ...
Verified Answer:
Question: 1.P.3
Find the equation of the tangent line to the cubic polynomial y =x³ at the point (-1,-1). ...
Verified Answer:
Let Q = ( x, x³ ) be another point on the graph of...
Question: 1.P.2
Find the equation of the tangent line to the parabola y = x² at the point (0,0). ...
Verified Answer:
Let Q = ( x, x²) be another point on the graph of ...
Question: 1.P.1
Find the equation of the tangent line to the parabola y = x² at the point (3,9) . ...
Verified Answer:
Find the equation of the tangent line to the parab...
Question: 33.2
Finding an Antiderivative Calculate ∫1/1-sin x dx. ...
Verified Answer:
It is not obvious how to proceed. The trick here i...
Question: 33.1
Two Similar Integrals Calculate the integrals: 1. ∫4/x²+9 dx. 2. ∫4/x²+9 dx. ...
Verified Answer:
1. For this integral you use the arctangent rule: ...
Question: 32.2
The Area ofa Surface of Revolution Set up the integral for the area of the surface formed ...
Verified Answer:
In this case, the radius is r(x) = x³ . Since f′(x...
Question: 32.1
The Length of a Line Segment Find the length of the line segment from (0,0) to (3,4). ...
Verified Answer:
You already know that the length of the segment ca...
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