Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) - 2 cos(r)- √2

Q: 3. Let f(2) = if z + 2i, while f(2i) = 3+4i, is f(2) continuous at z = 2i? 2- 2i 4. Evaluate lim (az…

A: 3)Given:

Q: Q:Discuss the continuity of the function f(x) =lim+ sinTt x)" - 1 n- (1+ sinTt x)" +1 at the point x…

A:

Q: Determine lim f(x) assuming that cosx < f(x) < 1.                   x→0

A: We first apply limit x approaches 0, on all sides of the given inequality.

Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

Q: If lim f(x) = = co then f (x) XCOS cos² X00

A: Given- If limx→∞fx=∞ then fx=xcos1x To Prove- The above expression.

Q: Suppost The following poroperties: f(x) = Trx, lim f)=2 that a function satifies %3D Find f(0), What…

A:

Q: Find the limits

A: Find the limit limx→-πx+4cosx+π

Q: Use the Squeeze Theorem to show that lim x2 co X-0 cos(207TX) = 0. Illustrate by graphing the…

A:

Q: Q2: Evaluate: [1] 21 lim m COSXVI+ COSX – v1-x, sin-1(x) V1+x - [3] lim-o

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: Find the value (1) lim (x,y)-(2-3) (3) lim (xy)-(11) √x-√√y of the following limits: x²-2xy + y²…

A: As per the instruction, post the question again for question (5). For (1),    limx, y→2,…

Q: E< -2 Let F (x) os (z + 2) -2< a' Cos Find lim F(z). E→-2+ lim F(z) = z→-2+

A:

Q: If 6 – 4x <g(x)<6 cos x for all x, find lim g(x).

A:

Q: Evaluate cot x – cos x lim z¬7/2 (T – 2æ)°

A:

Q: Let s(x)=sin(x)/x. Explain why it is true that Lim (X-> 2pi) s(x)=0

A: Let  sx=sinxx Explain why it is true that limx→2πsx=0

Q: :-√√3x lim x-3 27-x3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…