B. If limf (x) = 7, which of the following must be true? エ→3 I. fis continuous at x= 3 II. fis differentiable at x = 3 III. (3) = 7 None Il only C III only I and II only D. III pue 1 a

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A: To evaluate the given limit

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A:

Q: Which of the following is equal to the limit limx→0 sin^2 2x/xtanx A.  0  B.  4  C.  2  D.  8

A: We have to find the limit Use l'hopitals rule to obtain the limit. Keep on differentiating the…

Q: C. Find the following limits: 1) limy-o 2ytan(n/y) sin(n-02) 2) limo2→n Tøl-V

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Q: b* – 1 Show numerically that for b = 3 and b = 5, lim аppears to equal In 3 and In 5, respectively.

A: Given : limx→0bx−1x

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Q: In the given equation as follows , determine whether the statement is true or false. If it is false,…

A: f is continuous function on [0,∞) and ∫0∞f(x)dx diverges

Q: Which of the following expres zy 0 = .lim(z,9)¬(0,0) F+ y²

A: Let us substitute: y = mx Then we get, Limit as (x, y) tends to (0, 0), [(xy)/(x2 + y2)] = Limit as…

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Q: O Find lim (X,Y)→ LD,0) **+3y* or show it DNE.

A:

Q: Q3// Evaluate (a) lim,4 VE-2 S-V49 sin 3y cot 5y (b) limy-o y cot 4y

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Q: Let y(t) be a solution of ý = y(1 – ) such that y(0) = 6. Determine lim y(t) without finding y(1)…

A: Now,

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A: As we know that the expression for the slope of the tangent to the curve is:   limh→0fx+h-fxh…

Q: 1. Determine the following limits, or clearly explain why they do not exist. 3 - t+ sint (a) lim L…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: (d) Determine the following limit using u-substitution method: sin(t - 1) lim -1t2 +t – 2

A:

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A: Use the polar coordinate substitution

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A:

Q: 3 of 20 Select the best answer. (2e + 1)ª lim z+00 (tan(x))- O DNE

A: We have to find the limit.

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A: Given,

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A:

Q: Evaluate the limit: 1-Cos(9h) lim h h >0

A: Find the limit When we plug in 0 for h, the denominator becomes 0 So it is undefined.

Q: Choose the correct answer for the following limit S sin t3 dt lim 2 x4 (A) (B) (C) 1 8. (D) 4 (E) -4…

A: Given,

Q: (-cx² + 2x, (sin x + cos x, x> n x<π 9) Prove that lim (x* sin+5) = 5 10) f(x) = What value must c…

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Q: Find the limit of the following. V3 sin 0 lim 0→t/3 3

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Q: Show that when T(z) = az+b cz+d where (ad - bc ‡ 0), find lim T(z) = ∞ if c = 0. 7-3

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Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

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

Q: Evaluate the​ limit, where a and b are constants with b≠0. lim x -0 sin ax/ sin bx

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Q: If ƒ' is continuous on [0, ∞) and lim→∞ f(x) = 0, show that I p'(x) dx = = -f(0)

A: First we will integrate then put limit

Q: az? + sin y f(x, y) = and let L = lim(z,p) >(0,0) f(x, y). Which 29z² + y? of the following…

A:

Q: 8. Consider the solutions Y(t) of Y'(t) + ay(t) = de-bt with a, b, d constants and a, b > 0.…

A:

Q: 4) If y = (x² + 1)cos(3x), then find dy/dx. 5) Evaluate the following limit e cosx – 1 lim x-n/2 2x…

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Q: (4x 5y) (z,y)→(1,1) 5x2- 7y lim O 1/2 O 1/2 O Limit DNE

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A: we need to calculate Limx→π sin(πcos(x))Now we will substitute x = π to get answer .

Q: 1) Find the following limits. Do not apply L'Hospital's rule. r² + x – 6 lim 1+2 r? – 2.r (a) (b…

A: (a).  We have to find:  limx→2 x2+x-6x2-2x

Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

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Q: Evaluate the limit, using L'Hôpital's Rule if necessary. In(e6t – 1) dt lim X> 00

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Q: S 10 – x – a? if x 1 Calculate the following limits. Enter "DNE" if the limit does not exist. 2x +…

A: The given function is f(x)=10-x-x2if x≤12x+6if x&gt;1 We have to calculate,  a) limx→1-f(x)=?b)…

Q: S (2t)*dt lim x→ =? х* — 1

A:

Q: Q2: (a) By using " L' Hopital rul (1) limx¬(1/2)-(tan x)cos x

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Q: By using The definilion of the D Lim x (X+1)= o 2) Lin x Cos

A: Given: 1)limx→0x(x2+1)=02)limx→0x cos1x=0

Q: 2. Let x E (0, 1), use e – d to prove V4 +x – 2 lim 1 4

A: 2. Given x∈0,1, limx→04+x-2x=14                       ... (1) Use ε-δ definition to prove above the…

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A: We have to find limit

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A:

Q: If f' is continuous on [0, ∞) and limx→∞ f (x) = 0 , showthat

A: Given, If f' is continuous on the interval [0,∞) and limx→∞f(x)=0 show that, ∫0∞f'(x)dx=-f(0)