1. Evaluate the limits. e' cos (t – 4) dt - 4 (а) lim x2 x2 – 4 e2 + 2 (b) lim x00 e2x + 100

Q: Let f(x) = 1²-16 +4 1²-16 H-4 x > 0 I≤0 Find lim f(1)

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Q: 1. Let f(x) = 3² – 2x + 1. Compute lim (x)f – (4 + x)f 0+-4

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Q: f(x) – f(c) If lim exists, it equals the slope of the х — с to the graph of f at the point (c,…

A: If    limx→cf(x)-f(c)x-c  exists;

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: Let f(x): = lim_ f (x) Find →→3 a b x²-9 x + 3 x² - 9 X 3 с d if x 0 -6 0 does not exist 1

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Q: 3. Sketch the graph of a function y(x) with domain (-x, 0) that appears to satisfy each of the…

A: Given: The domain of the function is all real number,  limx→∞y(x)=5limx→-3y(x)=-∞limx→4y(x) does not…

Q: Suppose f(x), g(x), and h(x) are continuous functions such that g(-1) = 4, h(-1)=3 and lim…

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Q: 1.Find f'(x) using the limit definition of f'(x)= lim (x+h)- f(x) for the following function: f(x) =…

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Q: x² 1) Let f(x): = (Figure 24). Verify the following: x - 1 (a) f(0) is a local max and f(2) a local…

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Q: 2. Use the paths x = y and x = 0 to verify the limit. lim (x.y)-(0,0) x2+y²,

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Q: Consider the function 1– cos(x) f(x): (a) (T) Evaluate lim, →0 f(x) = L. (b) (T) As x → 0, at what…

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Suppose f(x) and g9(z) have the following values: • f(- 7) = - 6 and f'( – 7) = 1, • 9( – 7) = 1 and…

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Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

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Q: 2. For h(t)= Vt +12t – 2r² evaluate each of the following limits. (a) lim h(t) (b) limh(t) 『→の

A: We will find out the required limit.

Q: Suppose f(x) and g(x) have the following values: • f(8)= -4 and f'(8)= -6, g(8) 1 and g'(8) = -3. =…

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Q: 3. Let f(x) = x and P = {0, nn = 1}. ... + f("1) and that lim Lf(P) + k = k(k +1)/2) 1 Show that…

A: Given the function f(x) = x & a partition of the interval 0,1 as P =0,1n,2n,3n,...nn=1. First we…

Q: Let f and g be real-valued functions defined on (b, ∞). Suppose that limx->∞f(x)=L and…

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Q: Suppose we define g(x) to be a function in which Va 0 is small (in other words, when x is slightly…

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Q: Find lim f (x) if, for all x, 9 cos (4x) <f (x) < 8x2 +9. lim f (x) = %3D

A: The given inequality is: 9 cos(4x)≤f(x)≤8x2+9

Q: 2. g(x) 12(x – 3) х — 9 (a) lim g(x) (b) lim g(x)

A: Given that: g(x)=12(x-3)x-9