5. Evaluate the limit, if it exists. Show all work done in arriving at your answer. (a) lim(3x³ + x²-x+1) x-2 (b) lim sin (x + cos (x)) x-z (c) lim h→0 (d) lim h→0 (e) lim x--2 (f) lim x-0 √9+h-3 h (5+h)²-25 h x +5x+6 x + 2 1-√√1-3x² f(x) 6. Evaluate the limit, given that lim f(x) = −3 and limg(x) = )=5: lim- x-7 7 g(x) =

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A:

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A: L'Hospital's rule a.

Q: 4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim…

A: First we need to understand definition of limit:

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A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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Q: 3. (a) Differentiate the function f(x) = x2 from first principles.

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A: Given: limx→1f(x)-8x-1=2

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

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Q: 2x2 + x +7 if x -2 (a) Find lim f(x). x→-2- (b) Find lim f(x). x-2+ (c) Find lim f(x), or show that…

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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