Changing the order of integration Rewrite the following integrals using the indicated order of integration and then evaluate the resulting integral. 41. ∫ 0 1 ∫ 0 1 − x 2 ∫ 0 1 − x 2 d y d z d x in the order dz dy dx
Changing the order of integration Rewrite the following integrals using the indicated order of integration and then evaluate the resulting integral. 41. ∫ 0 1 ∫ 0 1 − x 2 ∫ 0 1 − x 2 d y d z d x in the order dz dy dx
Solution Summary: The author explains that the integral can be rewritten as 23.
Changing the order of integrationRewrite the following integrals using the indicated order of integration and then evaluate the resulting integral.
41.
∫
0
1
∫
0
1
−
x
2
∫
0
1
−
x
2
d
y
d
z
d
x
in the order dz dy dx
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
4. Suppose that the population of a certain collection of rare Brazilian ants is given by
P(t)=(t+100) In(t+2),
Where t represents the time in days. Find and interpret the rates of change of the population on the third day
and on the tenth day.
Find all values of x for f (x)=(x²-4) 4 where the tangent line is horizontal.
5. Find the slope of the tangent line to the graph of f(x)=-√8x+1 at x=1. Write the equation of the tangent
line.
3. Find the derivative of each function. Label with appropriate derivative notation showing both dependent and
independent variables.
f(t)=4t(2t⭑+4)³
a. f(t)=4t (2t+4)³ (Answer must be factored.)
b.
y=
3
1
(2x³-4)
6
Chapter 13 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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