xS -1 If s(x)={ find "e" so that Lim f(x) exists. x > -1

Q: lim (1-e X-

A: Limiting value of function is the value achieved by function when variable tends to approach certain…

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A: It is given that,  limx→0xcosx-1sinx-x We have to evaluate it.

Q: 8. (x - 1) dx √x lim

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Q: (5х-4, E If f(x) = 0<x <1 show that lim f(x) exists. %3D 4x - 3x, 1<x<2

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Q: Q 3/ x²-3 A- Find limx-3 x-V3. B- log10(3x – 7) + log10(3x + 1) = 1+ log10 2

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Q: 1 1 (b) lim x-0 'tan x e* – 1 -

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Q: 1 a. lim X-0* X

A: Given: limx→0+1x4

Q: 18. lim x+oo 3 20. lim log,

A: Given function f(x)=log12 x we write    log10 x=  log x     and we know thhat    log10 10=1

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Q: b. lim cos(x)-1 x2

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Q: If you initially invest $1 at an interest rate of 2% compounded n times per year, the value of the…

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Q: b) Find two functions such that lim, 0 f(x) = 0 lim, 0 g(x) = 0 but lim, 0 f(x)g(x) = 1

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Q: Find the limits in Exercise

A: The limit x→a+ implies x  approaches a from the right. The limit x→a- implies x  approaches a from…

Q: Using the definition of the derivative, find f'(x). Then find f'(-3), f'(0), and f'(4) when the…

A: f(x)=2x3+10

Q: sin (7x) Find the limit lim 2->0 x(Vr +2 – v2) x→0

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Q: 16. Find the equation of the line tangent to the functionf (x) = 6Vx at x-4. *hint: use lim,a…

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Q: (a) lim sih 7x (b) lim x 0 sin 7x x - 9 (c) lim x-9 x - 3

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Q: a. Find the Domain for y = = /4 -x + ! b. For what value of (k) is the function y-f(x) continuous at…

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Q: 2x+1 if x 2 Determine the one-sided limit lim f(x). x-2- 2

A: The given function is:

Q: (e) limVx ) lim -+(-1)") X-00 n→0 n n²-12345 x2 +9 (g) lim n +1 (h) lim x∞x3 +1

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Q: f (x+h)- f(x) 7x3-2x-1 Using lim-0 Find the slope of the tangent line y 5x+2 h at x = -1.

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Q: Find x/2 x-3 lim 148 x+1 O limit does not exist e^-2 Oe^-4 0-2 O-4 O Other:

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Q: 1+t-V1-t lim

A: To evaluate: limt→01+t-1-tt   if we substitute t=0, we get 00 (indeterminate form)   Consider…

Q: 5. Evaluate lim sin(x)– (x² + 3x – e*). (x³ – 2x2 - 6 + 3x) 6. Evaluate lim X→2 х - 2

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Q: 1-cos (x-m) lim

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Q: (1 – V3x lim tan- 3 + x x-00

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Q: 1 lim x-5 I. Find

A: For x-&gt;5^+ , x-5 -&gt; 0^+So denominator equals to 0.We can not find the limit by plugging the…

Q: 15x 5. Find lim using special limits. X→0 sin 3x

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Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

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Q: d. lim h(x) Preview e. lim h(x) = x→00 Preview f. lim h(x) = 00--x

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Q: xsinx lim x→0 e*+e¯x-2cosx

A: Since, we have been given up the expression:-limx→0 x sin (x)ex+e-x-2 cos (x)-(i)Since,on applying…

Q: S 1.4x + 0.8, x -2 f(-2) = lim f(x) = x--2- lim f(x) = x--2+ lim f(x) = || x--2

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Q: Evaluate limx=0+ e(1/x)

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Q: (220_ 3.x)– (e20_3e) lim -3x is x-e

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Q: |x| lim e* +- + x2 X→0-

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Q: 7- sin-(e*) 2 lim V1 - e2x

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Q: 1 X

A: Consider the limit

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Q: x² +1 if x -1

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Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

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Q: x² + 1 x – 1' if x -1 | бх — 4 3x² + 4x 1 O Evaluate: lim x2/3 + Зх + 2 4

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Q: 3 (а+h)2-За? Algebraically calculate the exact limit: lim h→0 h

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Q: x4/7 – 1 lim f'(a) where x→-1 x + 1 f(x) = and a = x4/7 lim x + 1 1 х>-1 II

A: Explanation of the solution is given below...

Q: 399. [T] lim e(x - 1) x-1 x-1

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Q: Q.No 3.) if x<-1 Let f(x)={ax+ B if -13x<1 x² +2 if x21 Find a and B, so that lim f(x) and lim f…

A: Given that, Consider, limx→-1-f(x) = limx→-1- x3 = (-1)3 = -1 limx→-1+f(x) = limx→-1+ (αx+β)=…

Q: x2 - 144 = 24. 1) Give an e-d proof of lim x- 12 x→12

A: proof of The proof, using delta and epsilon, that a function has a limit will mirror the definition…

Q: Along the path x = e" find y +4xy lim (х.)- (1,0) Зх — у -3 does not exist O -2 -3 2 0 30

A: Explanation of the answer is as follows

Q: -x + 1,x 2 0 Let f(x) = {x² + sin x -,x <0' (a) Find left-hand and right-hand limits as "x"…

A: Consider the given information:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.