Let a > 0 be a real number. Prove that lim x“ sin = 0.

Q: compute lim as x goes to pi/2 from the right of (x-pi/2)tan(x)

A: Given f(x)=x-π2 tanx To find limx→π2+f(x)=limx→π2+x-π2 tanx

Q: find the limit or explain why it does not exist

A:

Q: Find the limits in Exercis

A: Find the limit: limθ→0sinθsin2θ Solution: We know that, sin2θ=2sinθ cosθ Evaluating the limit.…

Q: Evaluate using the Squeeze Theorem

A: To find the limit  limx→0tanxcossin1x

Q: Find the limit of the trigonometric function. lim sin8) X → 3

A:

Q: Plot the function and use the graph to estimate the value of the limit.

A: The formula of special limit is given by: limθ→0 sin θθ=1

Q: Evaluate the limit. lim (1+ sin(6æ))cot (= ) x →0+ ||

A:

Q: Construct a table to find the indicated limit.

A: let f(x)= limx→0 sinx2x

Q: Evaluate the limit.

A: To find: limx→π6xsin3x

Q: Evaluate using Theorem as necessary.

A: The given is the symbol of limits, hence the definition of limits helps to find the required. A…

Q: - Show that lim sin a =D0.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Prove that lim |x|sin(1/x) = 0.

A: We need to prove that limit of given function is zero.

Q: Evaluate the limit sin 2x lim 7x

A: limx→0 sinxx = 1

Q: Find the limit of the trigonometric function.

A: limx→3tanπx4

Q: Find the limits in Exercis

A: Given: L=limx→0x-xcosxsin23x

Q: 2. Use Squeeze Theorem to evaluate lim sin(sinh x) csch x 8118

A:

Q: Find the value of the limit: 3 tan(4x)– 12x lim

A: From the given problem:   limx→03tan4x-12xx3   This problem can be solved by the series expansion of…

Q: Show that lim [x2 sin (1/x)] = 0.

A: Given: limx→0x2sin1x

Q: - lim a sin

A: We have to find limit using l'Hospital Rule

Q: Find the limits in Exercise

A: Given, limθ→0cosπθsinθ we know expansion of sinx sinx=x-x33!+x55!-.... now put this expansion in…

Q: (a) Show that tan x = sec?x using quotient rule. dx x+8 (b) Find lim X-2 x+2

A: Solution-

Q: Show that lim sin( does x→0 x2 .not exist

A:

Q: Find the lim using l'Hospitals Rule tan (7x). Sin ( 8x) lim X>0

A:

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DI lim -0.2x sin x X--0

A:

Q: tan Ø 10) lim Ø→0 sin2Ø

A:

Q: Q. Prove that: Lim tanhx =1 .

A:

Q: Find the limit, if it exists. sin(4x) x Ilm

A: To find the following limit, if it exists.limx→∞ sin 4xx

Q: Find the limit or prove that the limit does not exist. lim_(x→0) sin(1/x)cos(1/x)

A: In the given problem we have to find the limit of prove that the limit does not exist.…

Q: Find the limit: (а) lim tan 3x x2 sin27x

A:

Q: Show that lim |x|cos 0.

A: We have to prove that limx→0xcos1x4=0. Use property, if limx→a−fx=limx→a+fx=L then limx→afx=L. First…

Q: What is the lim, 0+ sin(y) In(y)?

A: limy→ 0+sinylny=limy→ 0+lny1sinyBy L'Hopital's rule,=limy→ 0+1y-cotycscy=limy→…

Q: Use Squeeze Theorem to evaluate lim x → to COS X loga x

A: To use squeeze theorem to evaluate the below limit. limx→∞cosxlogx2

Q: Prove that lim sin( nx) + n dx= In 2 . (n+) Explain your answer carefully

A:

Q: Compute the indicated limits. sin(2x) lim 3x

A:

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

A: Topic:- limits

Q: Find the value of lim tanx

A: As per our guidelines we only solve question number 1 . If you want the solution of other parts…

Q: Prove lim sin (t)

A:

Q: Show that lim x|cos )= = 0.

A:

Q: evaluate using Theorem 2 as necessary.

A: We rewrite the given expression as:

Q: Use the relation lim sin 0 = 1 to determine the limit. 0→0 tan 3x lim sin 8x

A:

Q: Evaluate the limit sin 9x lim I0 sin 3x

A:

Q: Evaluate the limit. In x lim x -1 sin 8TX

A:

Q: Evaluate lim→» V3 - cos x

A:

Q: Evaluate using Theorem 2 as necessary.

A: Given limx→0sinxsecxx

Q: By using Sandwich Theorem, prove that lim sin x

A:

Q: lim e^(sin(2022n)), as n goes to infinite, should this limit exist or not?

A:

Q: find the following limits if exist:- limx-0 1-cosx x sinx

A:

Q: Evaluate using Theorem 2 as necessary.

A: Given: limx→0 x2sin2(x)

Q: Evaluate limt-->0 (sin 3t)/(sin 6t) WITHOUT using L'Hospital's rule.

A: The given function is limt-->0(sin 3t)/(sin 6t).

Q: Evaluate lim (sin x)" エ→号一 tan z

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.