The exponential function V-e increases on the interval The logarithmic function y = ln ( x) incre...
Please show work 1.For the function f(x) = ln(x + 1) find the second Taylor polynomial P2(x) centered at c = 2. (9 points) 2. Use the Maclaurin series for arctan x to find a Maclaurin series for f(x). 3. Find the radius of convergence and the interval of convergence of the power series. We were unable to transcribe this imageWe were unable to transcribe this image
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.5. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state the interval of convergence. d) (3 points)...
# 2,3,4,7, 10,11,15,18) Differentiate the function: #2 f(x) = ln(22 + 1) #3 f@) = ln(cos) #4 f(x) = cos(In x) #7 f(x) = log2(1 – 3x) #10 f(t) = 1+Int #11 F(x) = In( 3+1") #18 y = (ln(1 + e*)] # 23) Find an equation of the tangent line to the curve y = In(x2 – 3) at the point (2,0). # 27, 31) Use the logarithmic differentiation to find the derivative of the function. # 27 y...
Use logarithmic differentiation to find the derivative of the function. y = (tan(x))2/ 4 cos ec(2x) y' = 2 ln(tan(x)) 2 Need Help? Read It Watch It Talk to a Tutor Submit Answer 13. [1/1 Pointsi TOT
(1 point) Find Taylor series of function f(x) = ln(x) at a = 7. (f(1) = (x – 7)") ܫ)ܐܶ Co C1 C2 = C3 = C4 Find the interval of convergence. The series is convergent: from 2 = left end included (Y,N): to = right end included (YN):
If we are given that the composite function g(x) = ln(f(x) passes through the point (0,1) where it has a tangent line of slope -1, then what is the value off'(0)? a) 0 b) 0-1 c) O-e d) e) Review Later Question 24 Find lim x? In(x2). X-0 a) 4 b) The limit does not exist. c) 0 d) 01 e) 2 Review Later
In(z) 3, Consider the function f(x)= (a) Find the Taylor series for r(z) at -e. b) What is the interval of convergence for this Taylor series? (c) Write out the constant term of your Taylor series from part (a). (Your answer should be a series!). (d) What can you say about the series you found in part (c), by interpreting it as the limit of your series as x → 0. (Does it converge? If so, what is the limit?)...
What is the average value of the function f(x)=e^3x on the interval [0, ln(2)]?
Please answer all, be explanatory but concise. Thanks. Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. Consider the differential equation y'(t) - 4y(t)- 8, y(0)4. a. Find a power series for the solution of the differential equation b. ldentify the function represented by the power series. Use a series to...
please do 9 Find a function f(x) with power series f(x) E-1n3 x" 9. 10. Use a power series to show that 0.999...= 1 n(1+1/n) 11. Determine the convergence/divergence of n-11+1/0 12. Find the length of the curve c(t) (Tt+e,2 cos t,2 sin t) for 0t T (1+3) converge? 13. To what value for the sequence an 14. Does the series ne- converge?V 15. Give an example of u, v E R3 perpendicular and with no zero entries in Find...