Why does the limit as x goes to 0 of cos(1/x) not exist? Can use two different sequences: xn=1/(n*pi), and yn=2/((2n+1)pi) and show that lim cos(1/xn) ≠ lim cos(1/yn).

Q: Find the limits

A:

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

A:

Q: ,3x lim x→0 CO cosh(Зa)

A: By substituting cosh(3x) in givenimit we can get the required value of Function.

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

A: Given problem is :

Q: what is the limit of (cos(x))^4/x^2 as x approaches 0 from the positive side?

A: Given,

Q: Find f(a)  a=2

A: We know that the definition of derivative is: We write the given equation in this format and find…

Q: how can the limit : limn→∞ (n sin(πn)) be rewriten as, limn→∞π sin(πn/πn/)

A: These two values are not equal

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

Q: H(3)=6 and the limit as x approaches 3 of H(x) is 6. Mustache be continuous at (3,6)? State why.

A:

Q: Find the limit tan (x) cos(3r) lim sin (2x)

A: Topic:- limits

Q: 间 Chapter 10.7, Problem 3E Find the limit. 3. lim (e-3ti+ · (e-³¹ ₁ + 1/7j+( 1-0 sin j+cos 2tk)

A:

Q: Find f '(a). 5t + 11 f(t) t + 8 Step 1 To find f '(a), we will use the formula = lim t) – f(a) f…

A: From the given step 1 we get:

Q: Find limit   without using derivative

A: Given,

Q: In general, if f(x) Tn [ f(x) dx > T₁ Since, M is the area under ---Select--- OM,> 1⁰0 OM,> [ºr(x)…

A: As per the question we have given a function f(x) and if f''(x) < 0 on an interval x ∈ [a, b]…