*PLEASE DO IN MATHEMATICA* {:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of the derivative and LHo...
R programming Consider the continuous function r22r+3 ifr < 0 f(r)=r+3 12 +4 7 if 2 < x. T>r50 Write a function tmpFn which takes a single argument xVec. The function should return the vector of values of the function f(x) evaluated at the values in xVec Hence plot the function f(x) for -3 <x< 3. Consider the continuous function r22r+3 ifr
For the function f(x)= 5x-1 , Use the limit definition of the derivative to find f (2) Note: You should first use find the derivation of the function; then replace x by 2 in the final answer.
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y) = 2 - 2x + 5y - 3x?y at a point (3.4). a. Find f (3.4). b. Find f (3.4). f|(3.4)=0 (Simplify your answer.) 13(3.4)=0 (Simplify your answer.)
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks 3. Consider the function defined by...
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
#23. Use the limit definition of the derivative to show why f(x) = (x - 5) is NOT differentiable at x = 5. (Hint: Compare the left- and right-hand limits of lim nits of lim f(5+h)-f(5) 102.) Is f(x) = (x - 5)% continuous at x = 5? What does the tangent line at the point (5,0) look like? 0
the function y=f(x)={ 0-4), 14x+16, x20 x<0 Consider 1. (a) Sketch the graph off. (3 pts.) (b) Verify that the function is continuous everywhere using the properties of the definition and possibly calculating the limit at a particular point. (2 pts.) (c) Show f'(x) is not continuous at x-0. (5 pts.) the function y=f(x)={ 0-4), 14x+16, x20 x
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y) = 6 - 6x + 5y - 3x2y at a point (3,4). a. Find f,(3,4). b. Find f(3,4). 1,(3,4)=0 (Simplify your answer.) 12(3,4)=0 (Simplify your answer.)
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?)...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...