c) Find the limit of the following functions by using L'Hopital's Rule. (i) lim (cosec x (ii) ex + e-x – x2 – 2 lim sin?x – x2

Q: Find the limits. Are the functions continuous at thepoint being approached? lim x →1 cos-1 (ln √x)

A: We find the limit by substitution

Q: 9. Evaluate the limit. lim (1+ sin 3x)1/x x→0+

A:

Q: Find the limit using lim sinx 1. X-0 x 5) lim sin(sin x) x0 sin x A) -1 B) 1 C) does not exist D) 0

A:

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x 4 A) 을 B) 0 530 C) D) Does not exist

A:

Q: Find the limit. lim e 3t i е j + Sin2 tan(5t) k) t 0

A: The given expression is,

Q: 2. Use a table of function values to estimate lim in3x sin 3x sin3x -0.1 0.1 -0.01 b. 0.01 -0.001 c.…

A:

Q: Find the limit of the trigonometric function.

A:

Q: Determine the following limits analytically.

A:

Q: 1. Find the limit of the following functions: lim 00x/3+ cos x 1-cosx lim X-0 sin2x

A: To find the limit of the given functions

Q: Determine the following limits by using L'Hôpital's Rule, if exists. 1- x + ln x (a) lim 1³-3x+2 (b)…

A:

Q: B) Evaluate two of the following limits (Without using calcu 1 1) lim 1-cos2 x

A:

Q: use l’Hôpital’s Rule to evaluate the limit

A:

Q: lim 4 x→0 2 1 +sin (2) cos sin

A:

Q: (i) Evaluate the limit or show that it does not exist. 2xy lim (x,y) (0,0) x2 + 2y² (ii) If cos(xyz)…

A: Firstly we can find Limits and In second one we can find partial derivatives .

Q: Find the limit of the trigonometric function.

A: Given: limx→π2sin x To Find: The limit of the given trigonometric function

Q: x cos(2x) (c) lim x-0 sin(-3x)

A:

Q: Q1: Find the Limits of: Тan x 1- lim X+Sin x+VX 2- lim xo X+Sin x 3- lim vx2 + 1- Vx2-x

A:

Q: Evaluate the limit: sin(5x) cos(6x). lim x→0

A:

Q: C- The result of the following limit is lim 1-0 sin t² t f

A: limt→0sin t2t

Q: (b) Find the following limits. Do not apply L'Hospital's rule. x2-4 lim x+2 x-2 (i) sin (31) (ii)…

A: Explained below

Q: Find the limit of the transcendental function. lim x → T/2 4 sin x

A: Definition of limits helps to find the limit of the given function. The value is said to be the…

Q: Computing the derivative of ƒ(x) = x2 ex

A: Consider the given function fx=x2ex

Q: I/ find the limit of the following: 1- limx cos 2- lim V +x sin

A:

Q: 1. Find the limit of the following functions: x2/3+x-1 lim e x2/3 + cos² x 1- cosx lim- -+0 sin2x

A:

Q: Find the limit of the following functions: x²/3 +x=1 lim x-00 x2/3 + cos² x 1- cosx lim- x-0 sin2x

A:

Q: 1. To take the derivative of the following function. х т (1) y = m (2) y = x' log 2. To find out the…

A:

Q: C-The result of the following limit is sin t² lim 1-0

A:

Q: Q2.) Find the limit lim X+x cos x 1. X→ 0 sin x cos x

A: We find limit x+ x cos x lim X → 0 Sn x cos x

Q: Use l'Hôpital's Rule to find the limit. lim 0-0 4-4 cos 0 sin 20 OA. 2 О в. о OC. ∞ OD. 1

A:

Q: Evaluate the limit.

A: We have to evaluate the limit: limh→0sin 9hh We know that limx→0sin xx=1 So making same angle of…

Q: 8) Find the limit (exact value) a) lim Vy - 3y – y ytoo tan ax b) lim- x→0 sin bx (a ±0,b± 0)

A:

Q: Evaluate the​ limit, where a and b are constants with b≠0. lim x -0 sin ax/ sin bx

A:

Q: 6. Figure out the following limits without applying L'Hopital Rule. sin(r- 4) V2r -1-1 b. lim (2²…

A:

Q: (c) Find the following limit: Vx +1- 2 lim X-3 x(x - 3) V9x2 + 5 lim x-00 X- 1 cot 0 csc lim sin e

A: Given we have to find the limit

Q: cosx * sin? (3x) 2 2. lim x→0 x2

A:

Q: Q2.) Find the limit ( 1 lim X+x cos x 1. X→ 0 sin x cos x |x + 2| 2 - lim(x + 3) x-2 x + 2 lim sin…

A: solve using properties of limits

Q: tanx - x x-0 x - sinx 1. lim

A:

Q: What is the value of a if the limit of the function is 3, given by еах —1-ах lim X→0 ex2. = 3? -cos…

A:

Q: Find the value of a for which the limit sin (ax) – sin x – x lim x→0 is finite and evaluate the…

A:

Q: Find the limit. lim vx+11 cos (x + 3T) X-- 3T lim vx+11 cos (x + 3r) = →-3T Type an exact answer,…

A:

Q: Q1- Evaluate the limit :- 1- lim - ( - cos) (1+ sin ) ) (1 + sin±)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the limit. x² + y® sin х - у +7 lim (x.y)→(0,0)

A: Given,

Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x-0 sin4x 2- lim…

A:

Q: 4. Evaluate the following limits: sin x (a) lim x-0 x³-7x2+10x (b) lim x→2 x2+x-6 sin at (c) lim…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Find the limit: 1 – cos(x) lim x2

A:

Q: I. Evaluate the following limits. x sinh x 1. lim x-0 cos 3x -1

A: Since you have asked multiple questions, as per Bartleby guideline, we are allowed to answer only…

Q: -x + 1, x > 0 3) Let f(x) = sin x -,x < 0' (a) Find left-hand and right-hand limits as "x"…

A: we have given f(x).  We have to find the left hand and right hand  limit.

Q: Use l’Hôpital’s rule to find the limits

A: Let the given limit be L - L = limx→0 x2lnsecxUsing L-hospital rule, differentiating numerator and…

Q: O3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x→0 sin4x 2- lim…

A:

Q: (c) Find the limit of the following functions by using L'Hopital's Rule. (i) lim (cosec x x-0 (ii)…

A: Given: (1). limx→0cosecx-1x So, we can also write as: limx→0cosecx-1x=limx→01sinx-1x   ...We know:…