Prove that the following sequences are convergent, and find their limits. x(k) = (1/k, e'-k, –2/k²)' x) = (e-* cos k, k sin(1/k), 3 + k-2)' a. b.

Q: Which of the following limits represents f '(2) if f(x) = 2x + 3 O A. 2(2+h)´ +3-11 lim h→0 OB. (2x…

A: To check the limit representation of f’(2) of given function.

Q: The limit that defines k' (3), the instantaneous rate of change of k(x) at 3, and its correct value…

A: Given: The Limit defines k'(3) the instantaneous rate of change of k(x) at x=3

Q: In finding the limit for  (x)2/x as x→+∞ by L'Hospital rule, which limit should appear in the late…

A:

Q: sin 3t. ln(sint) −i+ In(tant) lim +0+ sin 2t - j + (tlnt)k

A:

Q: Find the limit of * sin(6x) limx→0 sin(2x)

A: Given problem is :

Q: How do we calculate the limit of limx→0  (sin(x))/(9x3), by using the Taylor approximation

A: limx→0  (sin(x))/(9x3)

Q: assuming it exists x+2 56x) assuming it exists lind f(x) 100 (43) J

A: Given  that  limx→∞f(x) =exists=L (say)  limx→∞ f'(x)=M (say)  We  have  to  prove  that  ∫1∞f(x+3)…

Q: t's important to be able to recognize limits related to "e" when you're solving problems with…

A:

Q: 7.A) Estimate the value of f'(1) by substituting small values for h in the difference quotient…

A:

Q: 9. Sketch a graph that has the following properties: (i) ƒ is continuous on (-∞, ). (ii) f'(x) 0 on…

A:

Q: If f' is continuous, f(7) = 0, and f'(7) = 10, evaluate f(7+ 3x) + f(7 + 5x) lim Limit:

A: Given  f' is continuous, f(7)=0f'(7)=10

Q: Find f'(a) using the limit definition for 1 f(x) = V6 – 5x -

A:

Q: f, there is a sequence (zn) in C - {1¹} such that : lim z, = 1, but f(zn) n n→∞ has no limit in C U…

A: Take sequence z(n) as Z(n) = 1 + {[(-1)^n)]/n}So that as n goes to infinity  Z(n) goes to 1 .

Q: If f' is continuous, f(6) = 0, and f'(6) = 11, evaluate f(6+ 3x) + f(6 + 5x) lim Limit:

A: The objective is to evaluate the limit.

Q: What is the limit as t goes to 0 of    4 tan^-1(t)

A: Topic:- limit

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.