8. The function f(x) = 4 – x² is both continuous and differ- entiable at x = 1. Write these facts as limit statements.

Q: 2) Evaluate the limit at x=1 for: x* + 7x2 – x – 2 f(x) x² – 5x + 4

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Q: 2. Compute the following limits at infinity and give reasons for your answers. 1 a) lim b) lim I00…

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Q: 7. The function f(x) = 4x³ – 5x +1 is both continuous and differentiable at x = 2. Write these facts…

A: Given: The function f(x)=4x3-5x+1 is both continuous and differentiable at x=2. To Write: as limit…

Q: Let f(x)={5x+1  x≠4               {1       x=4. What is f(4)? If f(4) does not exist, type: 99999…

A: The given function is

Q: Estimate the limit numerically. ++7,000x³+ 800,000 lim 2x° + 1,269x³ 8. O to∞ 2.

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Q: Evaluate the following limit in two different ways: with and without l’Hôpital’s Rule.

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Q: Calculate the following limit of f(x). x² + 6x + 9 lim x +3 X--3

A: Calculate the following limit of f(x) . In this we use L'hospital rule because here made a 0/0 form…

Q: Compute the following limits exactly. Vx+22 -10 lim X 78 X-78

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Q: Show that the following limit fails to exist by showing that the limit is different for two…

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Q: 2 Use the definition of continuity to show f (x) = is x+3 continuous at x=1. Whenever you find a…

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Q: Let f(x) = 4x² + 6x + 2. According to the definition, f'(x) lim h→0 (Enter the limit in reduced…

A: Given f(x)=4x2+6x+2

Q: Show that the absolute-value function y = abs(x) = |x| is NOT differentiable at x = 0. (Hint: by…

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Q: Evaluate the limit using L'Hospital's rule: e10x – 1– 10x - - lim x2

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Q: Express the following limit as an integral. 7 lim Σ (5(at)* + 4x; - 6) Δr over 12,61

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Q: What is the limit of f (x) = 1 as x → π?

A: The value of this function is equal to 1 regardless of value of x as we can see below in graph.  So…

Q: The limit as x approaches infinty of (x+3^x)/(x^2-3^x) Evaulate using L'Hospital's Rule providing a…

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Q: Find the limit. lim X-2 x+2 O 1/2 -00 O Does not exist

A: Answer is limit does not exist

Q: Solve the following limit by definition (ii) (4 – 2x, x 1 lim f(x) = 2 if f(x) = %3D x→1

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Q: I need help evaluating this limit. Please refer to the attached picture.

A: Before evaluating the limit, let's simplify the given function. Please see the white board.

Q: In finding the limit for  (x)2/x as x→+∞ by L'Hospital rule, which limit should appear in the late…

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Q: For which of the following functions does the limit as x → 2 exist?

A: Given: 1.limx→2x-2x-22.limx→2sinx3.limx→2x2-4x-24.limx→2x2+16x-225.limx→2x2+x2x-16.limx→2tanπx4

Q: (a) Determine the following limits without using L'Hôpital's rule. V7x° +4x -x² -2 lim x'-2x-3x+1…

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Q: If f(x) = tanx – x and g(x) = x3, evaluate the limit of f(x)/g(x) as x approaches zero.

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Q: Compute f'(x) using the limit definition. f(x) = 1 – 26x-!

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Q: What is the limit as x goes to 0 for (e^x-1-x)/x^2?

A: Please refer the attached image for complete solution.

Q: Compute the limit 1 a2 1 - x2 lim xa x а - What can you say about the derivative of f(x) = ?

A: Given limit :

Q: Show that the absolute-value function y = t(x) = |x − 5| is NOT differentiable at x = 5. (Hint: by…

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Q: If x > 8 and x n+1 - - for nEN. Then the limit of x is equal to 11 X 21

A: Given that, If x1>8 and xn+1=2-1xn for n∈ℕ. The objective is to find the limit of xn.

Q: What is the limit of f (x) = 1 as x → T?

A: Value of a constant function is always same irrespective of input.

Q: Prove that a function f is continuous at a limit point p iff the limit as x goes to p is f(p).

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Q: 5. Evaluate the limit: Vx +1 lim x→1 4x -4

A: Limit at a point exists if left-handed and right-handed limits exist and they are equal. Left-handed…

Q: find the limit as x approaches infinity of (1+2/x)^x

A: Find the limit as x to infinity,

Q: compute limit as x goes to infinity of xe^-x

A: Given,            limx→∞x e-x

Q: What is the limit of f(x) = 1 as x ➔ rr?

A: given fx=1

Q: 9. Determine the exact answer for the following limit analytically: Vx+1-2 lim- x-3

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Q: 1-√3-x 4. lim. x→2 4-x²

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Q: 5.3. Show that when a limit of a function f(z) exists at a point 2o, it is unique.

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Q: Compute the limit as x approaches zero of f(x)=(x^2+3x)/(x^2-x-12)

A: Given : Function f(x)=(x2+3x)(x2-x-12)   To find : Limit of given function when x approaches to…

Q: cos x – 1 + x² lim x4

A: Given: limx→0cos(x)-1+12x2x4

Q: Q1. Compute the following limits if it exists. √x+2-3. 1-lim( x-7 2-lim (7x²+x+1) x→∞0 4x²+3x

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Q: The limit fx= X2 XスT 2メ-ズ Cos X ,X < TI at Will be 1-itexisted and eanals T 2-It existed and equals…

A: In the question we have to find correct option.

Q: Let f(x)={−4x+3   x≠4               {3       x=4. What is f(4)? If f(4) does not exist, type: 99999…

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Q: 1. Prove the following limits x 4y4 G) lim (x,y) (0,0) (x²+y4)3 = Does not exist

A: Solution is given below:

Q: what is the limit as x goes to 0 from the right of x^11x?

A: Refer to the function we need to calculate the limiting value of x from the right of x^11x.

Q: Given a function f(x) = c, where c is some constant. Show that f'(x) = 0. (Hint: by limit…

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Q: 12 Show that the following limits do not exist. 1 lim X0x (a) (x > 0), 4,

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Q: 4х + 1 Let f(x) = X-2 (a) Use the precise definition of the limit (i.e. e, 8) to prove that lim f(x)…

A: To solve this question we need to apply the conditions of limit and continuity

Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

A: