1) Evaluate the following limits. cos r - x4 - 1 sin? 2x 3* + cos r a) lim b) lim -00 3+2 – 2* c) lim In (t1) cos (x2 + VT) d) lim (cot r) m In a 2-0+

Q: a) Find the limits of the following functions: i. sin 2x lim o 2x +x V+ 12-4 lim X-2 x- 2

A: To find the limits of the following functions : (i)  limx → 0 sin 2x2x2 + x(ii)  limx → 2 x2 + 12…

Q: Evaluate

A: Consider the limit Squeeze theorem states that if f(x)<=g(x)<=h(x) for all numbers and at…

Q: 1 2. lim cOs X -

A: The given function rewrite as

Q: Evaluate these two limits given below

A: We will find the limits.

Q: B: prove that lim cos0 = 1 ||

A: We have to prove that

Q: Find the limits

A: Find the limit limx→-πx+4cosx+π

Q: Find the limits

A: It is given that, limx→01+x+sinx3cosx.

Q: Find the limits

A: Given limit:

Q: )Use the Sandwich Theorem to show that lim cos x-1 =0. x2 Find f'(x) for f(x) = sec(vx2 + 1).

A:

Q: 7. Find each limit. . a) lim (2x +Vx² +5 7a. x-0 6x – cosx b) lim- x-* x+sin 3.x 7b. 2x c) lim 7c.…

A:

Q: Q2: Evaluate each of the following limits: 1-cos 3X 2)limx-0 9X2 x$sin 3) lim00 x*+1

A:

Q: Q3) Find: (1) lim, V1+cos 2x (2) lim-2 (x+ 2) 14-x2

A:

Q: Evaluate:* x + 4x lim x4x2 + 2x - 8 4/5 1/2 2/3 3/4 Differentiate with respect to x: * y = sec(x² +…

A:

Q: b): Evaluate each of the following limits: 1- cos* 3x 1)lim 9x2 x sin 5 12)lim r+00 xt + 1

A:

Q: 1+3x COS x - 2.) lim tan x

A:

Q: Evaluate lim cos(sin 0) O -1 O 1 O does not exist

A:

Q: Show that lim x|cos )= = 0.

A:

Q: 4. Evaluate the following limits: z+8z+5 limz0 a) 28+9z+10 sin(8z) lim 0 b) 8z

A:

Q: Q. 2. a) Find the limits of the following functions: 1. ii. sin 2x lim: x-02x²+x √x² +12-4 lim X-2…

A:

Q: ) Find all points of discontinuity, if any, for f(x) = 5-3sin x sin² 2x x-0 sin² 3x Find lim

A: 2) Given function is f(x) = 5/(5-3sinx)

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.