We know that F is an antiderivative of f, so to: O a) lim (F (b) - F(a)) a 0 Ob) lim (F (b)-F (a)) a-0 Oc) lim (F (a) - F (0)) S. f (x) dx is equal

Q: If lim (æ) – f(a) x - a | exists, then f is differentiable at a. Select one: True False

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Q: Given that f(x) = 2x² +1, find:“ f(x+h)- f(x) f(x+h)– f(x). lim h→0 h h

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Q: Use (8) definition to show that lim 2-0 Z 0.

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Q: points

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Q: 2. Use the graph of y = f(x) to answer the following. (a) lim f(x) = . 2 (b) lim f(x) = (c) lim f(x)…

A: Using graph: (a).  Left hand limit: limx→2- f(x)=5

Q: Find the value of lim f(x), if x→3- S8x2 – 3 |5х + 7 f(æ) = x 3 O 69 57 66 45 22

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Q: 2f(x)=x² x-1 f(x)+1 3. If lim f(x) = 2, what is the value of lim a) 0 b) 1 ? c) 2 d)

A: Given: Limit ( x-> 1) f(x) = 2  Need to find- Limit ( x-> 1) [ 2f(x) - x2 / f(x) + 1 ]

Q: Let a and b be constants in R. and If lim (f(x) - (ax + b)) = 0, what is the value of b? x→→∞0 b= =…

A: Solution to find the value of b  of this limiting problem is as follow.

Q: Let f(x) = x³ + x² – 6x – and lim (g of)(x). 1 and g(x) = 3. Find lim(f° g)(x) x→4

A: Explanation: Given that,  f(x)=x3+x2-6x-1g(x)=3       Concept Used: Composition of function:…

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: If lim f(x) = L, then f(a) = L. A) True B) False

A: We can find the value as below

Q: Suppost The following poroperties: f(x) = Trx, lim f)=2 that a function satifies %3D Find f(0), What…

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Q: Suppose f (x) -7x -3x - 8 Evaluate: lim f (x) x→5

A: This is question of limit and continuity Here we have to find limit of function at given value…

Q: Given: -2 <x < 0 x = 0 0 <x < 2 x = 2 2 < x < 4 (x + 1, 2, f(x) = -x, 0, х — 4,

A: Givenf(x)=x+1  -2&lt;x&lt;0            2         x=0          -x      x=2           x-4…

Q: Given f(x) = x² + Va, then f(4+ h) – f(4) - a) lim h>0 h f(æ) – f(1) x – 1 b) lim Note: write either…

A: This question can be solved using the concept of function and rationalization.

Q: Given h(x)= Vx +9 - 3 a) Determine the value of x where h(x) is discontinuous. b) Find lim h(x). X-0

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Q: If f (x) is continuous e (a,b], we define | f (x) dx= lim | f(x) dx . on Xa+ A True B False

A: Solution

Q: Given c= -1 and the graph of the function f below, use the graph to find lim f (x). Z-et Y 4 3 2 -2…

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Q: C-x= (x)f and g(x) Given:

A: Given that, fx=x-5gx=2x2 Evaluate limx→-3fgx

Q: x² - 1 if x 2 x→2* а) 4 b) – 3 с) 3 d) – 4

A: Given function is  g(x) = x2-1   if x≤2x+2    if  x &gt;2 the function is defined in two intervals.…

Q: If f(x) = 2x? – x + 2 , what is lim 2x2 – x + 2, lim 2x2 – x + 2, andf(2)? Is f(x)continuous at 2? O…

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Q: x2 2. Find lim x→0 2ª – 1

A: We want to find limit of the function.

Q: x²-49 X-7x²-7x 2. Evaluate lim: 3. Evaluate lim √x+1-3 X-8 x-8

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Q: |c- bx For f(x)= 1< a <b<c, 2bx + a a) Create an image for the function Feel free to make other…

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