Q2/ a) If f) = , what are the domain of f(x) and g(x)? sin 6x lim 0 sin 9x b) Find

Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: Evaluate using Theorem as necessary.

A: Given : The limit is limt→0 sin2tt .

Q: 1 o. = 0. Show that lim x² sin -| *

A: Use the property that -1≤siny≤1. Take y=1x, then -1≤sin1x≤1

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A: As per Bartleby's expert answering policy, we cannot answer more than one question so kindly post…

Q: Find the limit. sin?(9x) lim

A: L’Hospital’s Rule : If  limx→af(x)g(x) = 00 or ∞∞  (indeterminate forms) then  limx→af(x)g(x) =…

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A: what is the value oflimx→π cosx+sin2x+1x2-π2

Q: Use l’Hôpital’s rule to find the limits

A: The L’Hospitals rule is used to obtain limits of a function when it occurs in the indeterminate form…

Q: 2) Show that sinax _a lim x-0 tanbx b %3D

A: Show that  limx→0sinaxtanbx

Q: Hence, determine whether the function is continuous at x = 2x. ) Find the value of k such that the 5…

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Q: Which theorem shall be used to find the lim sin 60 0-0 20 Theorem 1:lim Sin X x-0 x 1 = 1

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Q: sin 3y lim y→0 4y

A: Since you have asked multiple questions in a single request we would be answering only the first…

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A: Limit of a function can be found at x→a just by evaluating value of the function at x=a, provided it…

Q: True or false: lim(sin) as x goes to infinity exists.

A: Given, limx→∞sinx Find in the following that this limit is exist or not.

Q: 2x sin-x lim х—0 еx — Х — 1

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Q: What is the value of cosx + sin2x + 1 lim x2 – 72

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Q: Evaluate: 1- cos(x) 3x2 lim Express your answer in 4 decimal places.

A: According to question,Given limit,limx→0 1- cos x3x2

Q: (c) Prove the value of lim Sin 3a o Cos 4Do NOT use L'Hospital's Rule.

A: The given limit is,

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

A: limx→0cos2x-1sinx

Q: Evaluate using Theorem as necessary.

A:

Q: cos(7x) – 3 + b lim- x-0 e2x – bx – 1

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Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: Find the limits. Are the functions continuous at the point being approached?

A: Given function is  Since, the function f(t) exists finitely at t=0, so we will evaluate the limit…

Q: Prove that lim x->0+ √ x [1 + sin2 (2 π/x)] =0

A: Given: limx→0+x1+sin2 2πx By using the property of limit, the limit of a product is the product of a…

Q: * Find the value of Tx³ + 2. lim [sin (- x3+1] -1 O

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Q: So sin() -=? lim, o

A: Given that:limx→0+∫0xsin(t2)dtx3

Q: sin x lim bx = ? Use L'Hospital's Rule

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Q: 14. Prove that sin x cos x from dx first principles and be sure to prove all limits used.

A: Proof of limit which is used to prove derivative of sin(x) is cos(x).

Q: . Does knowing that | sin (1/x)| < 1 tell you anything about lim (x,y)→(0,0) y sin -?

A: To find the limit of the problem

Q: Find the limit of the trigonometric function.

A: To find: The limit limx→5π3cos x. Formula used: Trigonometric reduction Formula: cos 2π-α=cos α…

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: (i) Evaluate In (1-z³) lim 2->0 sin (2z

A: We need to evaluate the limit If the value of the function after putting the limit is in the…

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: Prove limθ→0 sin (θ)/θ=1.

A:

Q: 3. Use Squeeze Theorem to evaluate lim 1-0+ sin(In r) In(sin æ)"

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Q: If A = [0, 2π] and A is measurable, prove that lim cos nx dx = lim [₁ sin nx dx = 0. n-∞ JA

A: Given that if A⊂0,2π and A is measurable, the objective is to prove that limn→∞ ∫A cos nx dx =…

Q: What is the lim (3)¯ I 7 sec (7x) cos(3x)?

A:

Q: Q1- Evaluate the limit :- 1- lim - ( - cos) (1+ sin ) ) (1 + sin±)

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

Q: 4 sin 7x lim x1 cos TX+x

A:

Q: 6.) Use Theorem 4 lim x csc 3x e 7.) Use Theorem 4 lim e -0 sin? e

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

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Q: The point can be generalized (1)In the limits of trigor become in shape sin ax lim = 1 %3| ах

A: on solving this we get

Q: 1 lim x→0 x sin x x2 О 14 O 1/7 О 16 O 1/5

A: To find limx → 0 1x sin x - 1x2

Q: A func tion f is given. sin 4x f(x) = 2.x Is f even, odd, or neither?

A: We have to find type of function if fx=sin4x2x We know that  if we replace x with -x and after…

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

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Q: lim sin (xt3) dt X 5

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Q: 1 Prove that lim dx exists and find its value. (1+x?)" 1/2

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Q: lim 1-3 (r-3) tan(9-x²) sin²(2x - 6)

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Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

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

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

Q: Find the limit of the trigonometric function.

A: Given, limx→2-sinx12 To solve the above limit.