x+4 Which will prove that f(x) = %3D x2+16 is continuous at C= -4? 1. f(-4)=0 II. lim f(x)=0 III. f(x)= lim f(x) x--4 x--4

Q: 20. lim_ v3 – x x→3-

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A:

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Q: Suppose g(x)=4x^2-lnx is the derivative of f(x). Compute Lim x->0 (f(x+1)-f(1)/x) Please show steps…

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Q: ® Find Lim X->2 x¥ _ 2x² - 8 x² - 4 (2 ,X +2 Lim 3X X→3 X- 3 -3 X+3 O Lim © Lim t- fo -) ,X EO X+2 2

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A: In the given question w have to prove that if the integration  limn→∞∫01fn(x)-f(x)dx=0then…

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Q: 3* –1 lim V1+x -1,

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Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim-(7/2)-(tan x)cosx (2) limy-0…

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Q: 1 Lim x→0* x0x 1 sin x

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Q: compute lim as x goes to infinity of ln(x)^1/ln(x)

A: Consider the equation

Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1…

A: Make tables of the values of ƒ at values of x .

Q: z² +et= 1-400 2z-e² 2* - 3* 17. lim- x-0 18. lim cotxln(x+1) x-0 16. lim-

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Q: (4+ 43) (x + 43) -(16 + 43)x limy→ -43 limx. x + 43

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Q: 5. lim V2x +1 X-4 6. lim -) ズー1 x-1 CABA 3x+4 if x <-3 AT 7. lim f(x), where f(x) = 2-4 ifx2-3

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Q: Fird the domain of f (x) = 2-Vx2-5 Solve lim x→-3 =? (Don't use L'hopital Rule) x+3

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Q: 1 lim sinx x2 x→0

A:

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim X0 sin 2x x2-16 2. lim X+4 (VI+5)-3

A: *to find :- limits, using L-Hopital rule.

Q: • lim In (tanx) -Lーえ • Lim V9x* + ax 2 4x-1

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Q: 13. lim f(x), where Sx+2 xS2 3x-5 x> 2 f(x) = 14. lim f(x), where Sx* - x +1 x 3

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Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

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Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

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Q: Find the limit.   Lim x→∞             (1+2x)5/2 ln x

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Q: 2x cos. X 17) lim --

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Q: Prove that lim x cos 4 = 0. X-0 -1 s cos(4/x)s 1 = -x s cos(4/x) s x*. since lim (-x*) = x-0 and lim…

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Q: -7x2 – 6x + 1 x<0 x 20 f(x) = 3 sin x Enter DNE if the limit does not exist. lim f(x) = 1 lim f(x) =…

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Q: f(x+Ax)-f(x), Ff(x) = v2x + 1, what is the lim Дх--0 Ax

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Q: Find the limits: x² – x - а. lim x→1 In x e* – 1 b. lim x→0 sin x .3 c. lim С.

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Q: 1. Prove using e-d definition. (d) lim (4x + 3) = 7 x→1 x2 – 9 = 6 - (e) lim x→3 x – 3

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A: