The first derivative of the function f ( x ) = 1 − e x + ( e − 1 ) sin ( ( π / 2 ) x ) is zero at least once in the interval [ 0 , 1 ] .

Question

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Answer 1

Question

Chapter 1.2, Problem 3E

a.

To determine

To show: The first derivative of the function f(x)=1−ex+(e−1)sin((π/2)x) is zero at least once in the interval [0,1] .

b.

To determine

To show: The first derivative of the function f(x)=(x−1)tanx+xsinπx is zero at least once in the interval [0,1] .

c.

To determine

To show: The first derivative of the function f(x)=xsinπx−(x−2)lnx is zero at least once in the interval [1,2] .

d.

To determine

To show: The first derivative of the function f(x)=(x−2)sinxln(x+2) is zero at least once in the interval [−1,3] .

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Answer 2

Question

Chapter 1.2, Problem 3E

a.

To determine

To show: The first derivative of the function f(x)=1−ex+(e−1)sin((π/2)x) is zero at least once in the interval [0,1] .

b.

To determine

To show: The first derivative of the function f(x)=(x−1)tanx+xsinπx is zero at least once in the interval [0,1] .

c.

To determine

To show: The first derivative of the function f(x)=xsinπx−(x−2)lnx is zero at least once in the interval [1,2] .

d.

To determine

To show: The first derivative of the function f(x)=(x−2)sinxln(x+2) is zero at least once in the interval [−1,3] .

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Answer 3

Question

Chapter 1.2, Problem 3E

a.

To determine

To show: The first derivative of the function f(x)=1−ex+(e−1)sin((π/2)x) is zero at least once in the interval [0,1] .

b.

To determine

To show: The first derivative of the function f(x)=(x−1)tanx+xsinπx is zero at least once in the interval [0,1] .

c.

To determine

To show: The first derivative of the function f(x)=xsinπx−(x−2)lnx is zero at least once in the interval [1,2] .

d.

To determine

To show: The first derivative of the function f(x)=(x−2)sinxln(x+2) is zero at least once in the interval [−1,3] .

Expert Solution & Answer

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Answer 4

Question

Chapter 1.2, Problem 3E

a.

To determine

To show: The first derivative of the function f(x)=1−ex+(e−1)sin((π/2)x) is zero at least once in the interval [0,1] .

b.

To determine

To show: The first derivative of the function f(x)=(x−1)tanx+xsinπx is zero at least once in the interval [0,1] .

c.

To determine

To show: The first derivative of the function f(x)=xsinπx−(x−2)lnx is zero at least once in the interval [1,2] .

d.

To determine

To show: The first derivative of the function f(x)=(x−2)sinxln(x+2) is zero at least once in the interval [−1,3] .

Expert Solution & Answer

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Answer 5

Chapter 1.2, Problem 3E

a.

To determine

To show: The first derivative of the function f(x)=1−ex+(e−1)sin((π/2)x) is zero at least once in the interval [0,1] .

b.

To determine

To show: The first derivative of the function f(x)=(x−1)tanx+xsinπx is zero at least once in the interval [0,1] .

c.

To determine

To show: The first derivative of the function f(x)=xsinπx−(x−2)lnx is zero at least once in the interval [1,2] .

d.

To determine

To show: The first derivative of the function f(x)=(x−2)sinxln(x+2) is zero at least once in the interval [−1,3] .

Answer 6

Chapter 1.2, Problem 3E

a.

To determine

To show: The first derivative of the function f(x)=1−ex+(e−1)sin((π/2)x) is zero at least once in the interval [0,1] .

Answer 7

Chapter 1.2, Problem 3E

a.

To determine

To show: The first derivative of the function f(x)=1−ex+(e−1)sin((π/2)x) is zero at least once in the interval [0,1] .

Answer 8

b.

To determine

To show: The first derivative of the function f(x)=(x−1)tanx+xsinπx is zero at least once in the interval [0,1] .

Answer 9

b.

To determine

To show: The first derivative of the function f(x)=(x−1)tanx+xsinπx is zero at least once in the interval [0,1] .

Answer 10

c.

To determine

To show: The first derivative of the function f(x)=xsinπx−(x−2)lnx is zero at least once in the interval [1,2] .

Answer 11

c.

To determine

To show: The first derivative of the function f(x)=xsinπx−(x−2)lnx is zero at least once in the interval [1,2] .

Answer 12

d.

To determine

To show: The first derivative of the function f(x)=(x−2)sinxln(x+2) is zero at least once in the interval [−1,3] .

Answer 13

d.

To determine

To show: The first derivative of the function f(x)=(x−2)sinxln(x+2) is zero at least once in the interval [−1,3] .

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 1.2 - Prob. 1E Ch. 1.2 - Find intervals containing solutions to the...Ch. 1.2 - Prob. 3E Ch. 1.2 - Find maxaxbf(x) for the following functions and...Ch. 1.2 - Let f(x)=x3. Find the second Taylor polynomial...Ch. 1.2 - Prob. 6E Ch. 1.2 - Find the second Taylor polynomial P2(x) for the...Ch. 1.2 - Prob. 8E Ch. 1.2 - Prob. 9E Ch. 1.2 - Use a Taylor polynomial about /4 to approximate...

The first derivative of the function f ( x ) = 1 − e x + ( e − 1 ) sin ( ( π / 2 ) x ) is zero at least once in the interval [ 0 , 1 ] .

Solution Summary: The author explains the Rolle's Theorem, which states that if fin Cleft[a,bright] is differentiable, then there exists a number

Videos

To show: The first derivative of the function f(x)=1−ex+(e−1)sin((π/2)x) is zero at least once in the interval [0,1] .

To show: The first derivative of the function f(x)=(x−1)tanx+xsinπx is zero at least once in the interval [0,1] .

To show: The first derivative of the function f(x)=xsinπx−(x−2)lnx is zero at least once in the interval [1,2] .

To show: The first derivative of the function f(x)=(x−2)sinxln(x+2) is zero at least once in the interval [−1,3] .

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Chapter 1 Solutions