Evaluate lim x--> infinity xe-x Justify your answer.
Evaluate the following limit using l'Hôpital's Rule. 7In x-7 lim X-e Xe Use l'Hôpital's Rule to rewrite the given limit so that it is not an indeterminate form. 7in x-7 lim X-e = lim Xe Xe Evaluate the limit. 7In x-7 7 = (Type an integer or a fraction.) lim X-e X-e n. Find the solution of the following initial value problem. p' (t) = 65 e -; (O) = 280 The solution of the initial value problem is p(t)...
Evaluate it
(b) Evaluate the limit lim (Vlog(x)) 10+ Make sure you clearly explain/justify each step in your working.
1 point) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges without being infinity or negative infinity, state your answer as DIV. lim n infty -17n+ 17 7^ n
x-4 a) lim x-2 X-2 xe* b) lim *-01-et lim (1+x)'* X+00
2. Let f(x)= V12-x-x?. Evaluate lim f(x). Justify each step by indicating the limit law(s) used. (10)
Evaluate lim ex, lim ex, and lime -X. X-00 X-00 X+00 lim ex = X-00 (Simplify your answer. Type an exact answer.)
(18. a) Evaluate lim e sin (b) Evaluate lim x sin x 0 x (c) Illustrate parts (a) and (b) by graphing y = x sin(1/x).
Let f(x)-1 if XE [-1/2, 1 /2) x 2 if xE[1/2, T] If FN(x) is the partial sum of the Fourier series of f(x), then give lim Fv(1/2)? Please give your answer in decimal form. (Hint: It might be helpful to sketch the function)
Let f(x)-1 if XE [-1/2, 1 /2) x 2 if xE[1/2, T] If FN(x) is the partial sum of the Fourier series of f(x), then give lim Fv(1/2)? Please give your answer in decimal form. (Hint:...
Evaluate the following limit using Taylor series. -X- In (1 - x) lim x→0 106² - x - In (1 – X) lim (Simplify your answer.) x→0 1082
3) Use L'Hopital's Rule to evaluate and check your answers numerically: - sin x (a) lim x+0+ х 1 (b) lim X-70