lim tan(3x) x-

Q: Find the limits in Exercises

A: limx→∞x+tanx+3x+tanx

Q: Evaluate using substitution.

A: We find the limit by substitution

Q: Guess the value of lim x 0 sinx/x

A: We try to find the limit by substitution  But 0/0 is indeterminate form.

Q: tan?x lim

A:

Q: Evaluate using substitution. lim 3 sin x x→ -π/2

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Q: Find lim(2 – x)tan(r2/2)

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Q: If 0 < a <1, then lim(a)* = x00

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Q: Š Add your answer In evaluating dx is same as evaluating lim (In(f(x)){§). Determine the value of…

A:

Q: tan 5x lim x-

A: Consider the following limit: limx→0tan5xx Apply L'hopital rule to the above limit:…

Q: lim (х — Vx? + х

A: Consider fx=x-x2+x. Simplify the above function. fx=x-x2+xx+x2+xx+x2+x=x2-x2-xx+x2+x=-xx+x2+x

Q: lim, 1 f(x) = %3D

A: limx→a f(x) =L if and only if limx→a- f(x) = L =limx→a+ f(x) .

Q: Find lim x→3- x2 – 9 for o, -inf for -o, and DNE

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Q: sec x lim X0 n x

A: Here we have to find the limit.

Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

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Q: Find the value of a . lim,2 sin a(x-2) 3 2-2

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Q: tan2x 4) lim, -X, 2 x- 2

A: Explanation of the answer is as follows

Q: Evaluate the lim x>0 Vx+1-1

A: Solve the given

Q: tan(14x) lim x→0 5x |

A:

Q: Q1: limx-→n tan(x) is X-T 1

A: Given, limx→ πtanxx-π

Q: tan (5x) lim x0

A:

Q: tan(x) Q1: limx¬n X-n is

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Q: LA Find lim ujs (Ад 10ex csch x

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Q: If 4- 3x sg(x) s4 cos x for all x, find lim g(x).

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Q: Q \ Find the value of 8 > 0 that guarantee lim x-0 csc(1/x) = 0 in terms of ɛ?

A: Definition of limit: We know that, limx→af(x)=L               ...(i) For each ϵ&gt;0, there exists a…

Q: 8x+4-4cos?x+tanx Q1) Find lim X-0 4sin2x

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Q: 2t – 1 Evaluate lim,, tan-1, e> - t - 1

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Q: Evaluate: lim- A. 1 B. e C. 0 D. DNE E. ∞ →2+ [(x² − 4) (-2)]

A: We know, ln(ab)=b*ln(a)

Q: Evaluate: tan(5r) a) lim 12z b) lim (cot(8) + csc(0))

A:

Q: Evaluate: lim (cos x)=¹2 X x → 0

A: Since the numerator is positive and the denominator x^2 approaches zero and is greater than zero for…

Q: neither lim f(x) nc

A: For the limit  fx and gx , take the condition . For function fx, fx=2 if x≥00 if x&lt;0 The limit…

Q: x?} シrlet Evaluate lim 1+2x +

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Q: In(x+999) =? b) lim h→0 (x+h)10 –x10 =? 1) a) lim In x h

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Q: lim (r + 4x? + 4x – 1) = -1, x-2

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Q: -1 X +1 M Evaluate : limx{tan X+4 4

A: We have to find

Q: Q2) find the value of each limit 1) lim(6x. sinx sinzx

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Q: Evaluate lim(1+ tan x)r

A:

Q: Evaluate lim w/ e 1- sin C x)

A: First , evaluate the limit. limx→∞ex3−1sin1x=limx→∞ex3−1limx→∞sin1x=e∞3−1sin1∞=e∞−1sin0=∞−10=∞0…

Q: ?? 13 Find lim (1-tan X/2) Secx

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Q: Q2. Do as required 3. Evaluate: lim (-) X0 sinx

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Q: x2ex b. Evaluate lim by using T.E. X-0 CoSX-1

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Q: use f(x) to find: limx→0f(x), limx→-4f(x), limx→5+f(x), limx→-4-f(x). the discontinuity that is…

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Q: 8. Evaluate lim sin7x. x0 3x

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Q: lim 2 +and 2.

A: Explanation of the answer is as follows

Q: What is lim (x? – 4x + 5)? O 1 O 2 O does not exist

A: To find÷limx→2 x2-4x+5    limx→2 x2-4x+5=22-42+5                           =4-8+5…

Q: tan(ху) = ? .2. (х,у) >(0,1) х*y+x lim

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Q: What is the lim f(x) where f(x) = {x" + 10x+24, if x -3 %3D X-3 A. 0 В. 3 С. 12 D. DNE

A: Given: fx=x2+10x+24, x≤-3-x, x&gt;-3   As we know that; The limit limx→afx exists when the left-hand…

Q: 4sinx pute lim,x»n sin2x

A:

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.