4. A Maclaurin series a. is a Taylor series that converges everywhere. b. is a T

Question

4. A Maclaurin series

a. is a Taylor series that converges everywhere.

b. is a Taylor series that is centered at x = 1.

c. is a Taylor series that is centered at x = 0.

d. is just another name for a Taylor series.

e. None of the above

5. The third degree Taylor Polynomial for f(x) = sin(x) centered at x = 0 is

a. 1 minus x^2/2!

b. 1 + x^2/2!

c. x minus x^ 3/3!

d. x + x^3/3!

e. None of the above

6. The third degree Taylor Polynomial for f(x) = cos(x) centered at x = 0 is

a. 1 minus x^2/2!

b. 1 + x^2/2!

c. x minus x^3 /3!

d. x + x^3/3!

e. None of the above

a. 1 minus x^2

b. 1 + x^2 minus x^3/6

c. 1 minus x^2/2!

d. 1 minus x^2 + x^3/6

e. None of the above

8. Find the Taylor series centered at 0 for f(x) = e^x^2

e.none of the above

9.Find the Taylor series centered at 0 for f(x) = integral e^x^2 dx.

e.nonw of the above

e.none of the above

11. The Taylor Series centered at x = 0 for f(x) = 1/(1minus x)^2 is

e.none of the above

a.1/5

b.5

c.5/2

d.2/5

e.none of the above

a. 0

b. minus 1

c. 1

d. the limit is undefined

e. None of the above

4. A Maclaurin series a. is a Taylor series that converges everywhere. b. is a Taylor series that is centered at x = 1. c. is a Taylor series that is centered at x = 0. d. is just another name for a Taylor series. e. None of the above 5. The third degree Taylor Polynomial for f(x) = sin(x) centered at x = 0 is a. 1 minus x^2/2! b. 1 + x^2/2! c. x minus x^ 3/3! d. x + x^3/3! e. None of the above 6. The third degree Taylor Polynomial for f(x) = cos(x) centered at x = 0 is a. 1 minus x^2/2! b. 1 + x^2/2! c. x minus x^3 /3! d. x + x^3/3! e. None of the above 7.The third degree Taylor Polynomial for f(x) = a. 0 b. minus 1 c. 1 d. the limit is undefined e. None of the above a.1/5 b.5 c.5/2 d.2/5 e.none of the above 13.Evalute e.none of the above 12.If f(x) has Taylor series d.c. b. e.none of the above 11. The Taylor Series centered at x = 0 for f(x) = 1/(1minus x)^2 is d. c. b. e.nonw of the above 10. d. c. b. e.none of the above 9.Find the Taylor series centered at 0 for f(x) = integral e^x^2 dx. a. d.c. b. e^-x^2 centered at x = 0 is a. 1 minus x^2 b. 1 + x^2 minus x^3/6 c. 1 minus x^2/2! d. 1 minus x^2 + x^3/6 e. None of the above 8. Find the Taylor series centered at 0 for f(x) = e^x^2

Explanation / Answer

4th --> option c is correct (is a Taylor series that is centered at x = 0.)

5th --> option c is correct (x minus x^ 3/3!)

6th --> option a is correct (1 minus x^2/2!)

7th --> option a is correct (1 minus x^2)

8th --> option b is correct ( sigma n = 0 to infinity, x^2n/n!)

9th --> option d is correct

11th --> option b is correct ( sigma n = 1 to infinity, n(x)^(n-1)

12th --> option d is correct (2/5)

13th --> option c is correct (1)

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