Suppose that lim f(x) = 0, lim g(x) = 0, lim h(x) = 1, lim p(x) = ∞, and x→a x→a x→a x→a lim q(x) = ∞. x→a Evaluate each of the following limits. (a) lim [f(x)]⁹(*) x→a = (b) lim [f(x)]P(x) = x→a (c) lim [h(x)]P(x) x→a =

Q: If g(x) is differentiable at x = 1, then lim g(x) = g(1). x+ 1+ True False

A: A function f(x) is differentiable at x=a, if limit exist at x=a and is equal to f(a)

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Q: 7. Use the definition of the limit of a function to show that if lim f(x) = a and lim g(x) = b, x→x0…

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Q: 1. Using the limit rules, find lim f(x) for the following functions: (a) f(x)= 3. (b) f(x)=¿e-2*.…

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Q: Let f(x) = 2/(2 – x) and g(x) = 8/(4 – x²) Find lim [f(x) –- g(x)] 7. a.

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Q: 5. Sketch the graph of one function y = f(x) that satisfies all of the requir- ments below. lim f(x)…

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Q: If lim f(x) = 2, and lim g(x) = 7 find: C→C I-C a) lim 4f(z) A C b) lim ln(g(x))

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Q: Let f(x) = x3+x. Evaluate lim s→0 (f(x + s) − f(x))/s .

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Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: x² – 9 (b) lim x→3- x + 3

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Q: If lim f(x) = 15 and lim g(x) = 25 then x5 x5 lim 3f(x)g(x) –- 6] = x5

A: Given that limx→5 fx =15  and limx→5 gx=25 find limx→5 3fxgx-6=?

Q: . Let (x2 + 1 f(x) = 1( - 2)² if x> 1 if x<1 (a) Find lim,-I- f(x) and lim,→* f(x). (b) Does lim ,1…

A: Given: For (a),     limx→1- f(x)=limx→1 x2+1=12+1=2 and     limx→1+ f(x)=limx→1 x-22=(-1)2 =1

Q: 7. Identify if the statement is Always True, Sometimes True or Never True. If lim f(x) exists, then…

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Q: Find lim f(x) and lim f(x) for the given function and value of c. X→c+ |x + 8| f(x) = (x + 9)- X +8…

A: Please see the below picture for detailed solution.

Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

Q: If lim f(x) = 16 and lim g(x) = 24 then x8 lim[3f(x)g(x) – 7] = O 1159 O 1152 O 1145 O 216 O 32

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Q: Suppose y = f(x) is the equation of a curve which lies between the curves y = x² + 3 and y = 621…

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Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: 1 (B). Evaluate lim (3 – x) x-2 x→2

A: Given that  lim x to 2 (3-x)^(1/(x-2))

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A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…

Q: 03 1 -5 -4 -3 -2 -1 2 3 4 5

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Q: 3. Sketch a graph of a function (x) for w ich all of the fo lowing are true: lim-2' f(x) = -4,…

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Q: Suppose ƒ: (0, ∞) → (0, ∞) is a function such that lim f(x) exists 2+0 and equals 4. True or false:…

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