Suppose f and g are continuous functions such that g(3) = 6 and lim [3f(x) + f(x)g(x)] = 45. Find f(3). X- 3

Q: Evaluate the limit of the function: lim f(x) =- /7 +x -V7

A: topic - limits

Q: Find Limit Using Squeeze Theorem 2. If 2x – 2 < f (x) < x² – 4x + 3 for x 2 0, find lim f (x). - x→1

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Q: If x3 f(x) s x for x in [-1,1], find lim f(x) if it exists. X-0

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A: Given limx→c f(x) does not exist because the left-hand and right - hand limit have different values.

Q: Vx+15 -2 is The value of the limit lim X+-11 x+11

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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: Suppose f(– 1) = 0 g( - 1) = 0 f'(– 1) = 5 g'(– 1) = 4 and all functions are continuous. lim…

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Q: 3x lim x→0 x2 + 2x

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Q: For all x ≥ 0, 4x − 9 ≤ f(x) ≤ x 2 − 4x + 7. Find limx→4 f(x). ⇒

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Q: Determine the limit by sketching an appropriate graph. 0 sx < 2 2 sx < 4 lim f(x), where f(x) = x-2-…

A: Given that f(x)=4-x2     0≤x&lt;22               2≤x&lt;44               x=4We have to find limx→2-…

Q: If f and g are continuous functions with f(-3) = 4 and the following limit, find g(-3). lim [4f (x)…

A: Given: limx→1f(x)-4x-1=7 Also f and g is continuous function with f(-3)=4  and limx→-3[4f(x)-g(x)]=9…

Q: 5. lim x-0 e2x-1

A: LetL=limx→ 0xe2x-1Plug in the value x=0L=0e2(0)-1L=01-1L=00Therefore Apply L Hospital ruleL=limx→…

Q: Let f(x) = 2x² + 2x + 3. According to the definition, f'(x) = lim h→0 (Enter the limit in reduced…

A: the soluton is following.

Q: Find the limits x² - 7x lim X-o X + 1

A: Given: limx→∞x2-7xx+1

Q: Find the limit, if it exists. 1) lim (x2 + 8x - 2) X→1

A: =?

Q: Find the limit. 3x + 5 lim x→0 x - 4

A: Find the limit  limx→∞3x+5x-4

Q: Find the limit. lim x→0 x – 1

A: Given that: limx→∞5x-1

Q: Find the limit.   Lim  x→1+      x1/1-x

A: Given function is By property of logarithm

Q: -f(x): a. lim

A: We'll answer the first question only since the exact one wasn't specified. Please submit a new…

Q: Find the limit as x approaches - 2 for the function f(x) = 12x + 1. %3D lim (12x+1) = X→-2

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Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: Find the limit of the function lim x² 3x +2 X-1 X-A

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Q: 4. Do you agree with the following statement? When a function f is continuous at a number a, then it…

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Q: Find the limit of the function lim x → − 2 ( 2 − | x | 2 + x )

A: Topic:- calculus

Q: 1 Use a plot of f (x) = 4 Vx - 2 to estimate lim f(x) 4 メ→4 | numerically.

A: Given: f(x)=1x−2−4x−4Estimate:limx→4f(x)=?Graphically  and  Numericallly

Q: Find the limit of lim((9+3x)1/2-3)/x as x approaches 0

A: To determine the value of the limit.

Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: Find the limit. lim (2 – x)3 tan(a) x→1

A: limit

Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

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Q: Show that the function given below is continuous. 4v2 - 16v lim -2 v-4

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Q: Let f(x) = Vx - 1 if x>4 and f(x) = x² – 4x + 1 if x < 4. Find: %3D lim f(x) x→4

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Q: find the lim as x approaches infinity when f(x)= (1-x)/2x

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Q: If 2x - 2s f(x) S x² - 2x + 2 for x 2 0, find lim f(x) x-2

A: see below the answer

Q: (2) Suppose that a function f(x) is defined for all real values x except x* x,, then lim f(x) does…

A: For limit to be exist at a point, left hand side and right hand side values of function should be…

Q: + 34, find f '(x) using the definition f '(x) = lim h→0

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Q: Find the limit. x* – 1 - lim x→0+ In (x) +x – 1 п lim ( 1+ n

A: These question is based on Limits.

Q: —ах+6 if x2-1 Let f(x)=< For what value of a does 2x2 +ах ifx<-1 lim f(x) exist? x--1

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Q: Find the limit, if it exists

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Q: Given f(x) = 5x³ + 7x + 7, write a limit representing the derivative of f(x) at x = −2. Provide your…

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Q: Find the limit lim x3 e-x2 X→00

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Q: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: . For a function f, suppose lim f(x) does not exist because values of f(x) oscillate between two…

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Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: f(0) = 1, f"(x) < 0 for x # 0, lim f'(x) = +0, lim f'(x) = -00

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Q: Find the limit x-1 lim x>I* Vx +2

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Q: Let f(x) be the function defined by x²+ 4x (xs3) 2x - 1 (x>3) the rule f(x) Find the one-sided limit…

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Q: Find the limits. f(x) = x + 3 g(x) = x2 (a) lim f(x) X→-1

A: A limit tells us the value that a function approaches as that function's inputs get closer and…