1 Calculate the following (possibly infinite) limits or show that they do not exist. Hint: Recall the differnece of squares property a2 – 62 = (a + b)(a – b) and that tan(x) can be written in terms of sin(x) and cos(x). x² – 49 (a) lim 7 x2 - 8x +7 sin(x) (b) lim 20 tan(x)

Q: 9- Solve the question. Lim cos(2x)/x X->T

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Q: b. lim cos(x)-1 x2

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Q: Given that –xª + 1< sin(x) < 3 – 2 cos(x), what is lim sin(x) :?

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Q: d) sin(arcsin [Select] (4³)) = 1/³ by the Cancellation Property of Inverses 2 2 e) arctan(tan(-g))…

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Q: (a) lim r0o In(x² + 5) In(x + 2) (b) lim(1+3 sin x)/ª. 2 cos x - (c) lim r1/4 1- tan x

A: I use L hospital's Rule

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Q: 3. Use two rectangles of equal width to estimate the area between the graph of f(x) = x + cos(x) and…

A: Solved below.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.