Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

Q: If lim f'(x) =0, then the graph of y= f(x) has a horizontal asymptote. %3D Select one: O True O…

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Q: 3. Sketch a graph of a function y = f(x) that satisfies all of the following (if possible): а. x-0-…

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Q: The limit lim h→0 f(x) = ab a= b sin (a) sin (a) In(e +h)-1 h 8 x α a represents f'(a) for some…

A: Topic:- application of derivatives and calculus

Q: lim at e -

A: Find the limit when x tends to 0

Q: Which of the following graphs below show that lim f(x) exists? x-3 34-x i ii iii

A: Limit of a function means the value 'p' function approaches when 'x' approaches 'a'.

Q: 2. Given the graph of the function f shown below, determine which of the following statements is…

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Q: b. lim x->0+ -3/x 2 X²

A: A limit is a value that a function approaches as the input approaches some value. Limits are…

Q: tan(3x) lim x→0 2x2 + 4x

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Q: Give two applications of the derivative f(x + h) - f(x) f'(x) = lim h

A: The given function f'x=limh→0f(x+h)-f(x)h is the derivative by first principle.

Q: 15.) Show that lim((2n)/"): 1/m =1.

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Q: Use the graph of the given function f(x) below to find the following. If something does not have a…

A: Solution:

Q: State the function and the number: f(x) = a =

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Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: 96. Sketch the graph of a function y = f(x) with all of the following properties: a. f'(x) > 0 for…

A: Using the given information drawing one of the possible graph of f(x).

Q: If 4æ – 11y = 5 is the tangent to f(x) f(x) - f(3) at a = 3, then lim | (A) =! (B) 규 (C) 4 (D) (E) 4…

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Q: Show that the GHASH function calculates (X1 • H™) Ð (X, · H"-1) © O (Xm-1° H²) O (Xm· H) ...

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Q: lim f(x)=-5 f. f'(-3)=0 а. g. f'(-2) is undefined h. f(-1)=2 i. f'(-1)=0 j. f'(3)=0 b. f'(-5) is…

A: When there's no tangent line and thus no derivative at a sharp corner on a function

Q: 2 ež h(x) 1 - 4 What is lim h(x)? x→+∞

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Q: x' + 2, if x 0 (a) Find lim f(x).

A: Since , the only point of discontinuity can be zero . For rest of the points on ℝ the function is…

Q: if x'(3) = 8 Sind Lim X(3 + 2h) - X (3-h) h->>0 h

A: The answer is given below:

Q: Let s(x)=sin(x)/x. Explain why it is true that Lim (X-> 2pi) s(x)=0

A: Let  sx=sinxx Explain why it is true that limx→2πsx=0

Q: find lim x-> 0, cos (12x)-1 / 3x

A: Given,              limx→0cos 12x - 13x Move the term 1/3 outside of the limit because it is…

Q: 62. Show that lim n→∞ 1 + X n n 63-78 Find the derivative of th - S e* for any x > 0.

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Q: 12. Let L = lim a>0. If L is finite, the (A) a=1 (B) a=2 (C)L- (D) L-

A: We are asked to find a value and L values.

Q: Find lim L(Sn(x – a)). You'll need L'hopital.

A: Using L'hospital rule