You may assume that the exponential and cosine functions are continuous and may freely use techniques from one-variable calculus, such as L'Hôpital's rule. Compute the limits. (If an answer does not exist, enter DNE.) (a) lim (x, y) (0, 7) cos(x) - 1 (b) lim X-0 x2 eh - 1 lim (c) h-0 h

Q: x sin(2x) 1- cos(x) limr→0 | А. О В. 1 С. 2 D. 4 E. the limit does not exist ||

A: The given expression is limx→0xsin2x1-cosx. Evaluate the limit limx→0xsin2x1-cosx as shown below.

Q: Find the limit, if it exists.

A: The limit of a function limx→Xfx=Y means that value of  function f(x) can be as close to Y by making…

Q: Prove that

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: -1- x +3, if x -2 Calculate the following limits. Enter DNE if the limit does not exist. lim f(x) =…

A: Given : fx =-1-x + 3   if x<-23                        if x=-22x+8                if x>-2

Q: Find the limit. y sin x limx.y)(0,1) O 1 8. O No Limit

A: Find the limit. lim (x.y)→(0,1) (y5 sin x)/x To select correct option  1 0 ∞ No Limit

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

A: Given: u=(1+sin(3x))1x We want to find  limx→0+u=limx→0+(1+sin(3x))1x Since we know that u=eln(u)…

Q: 1 Discuss the existence of the limit lim sin x 0 x

A: To determine: The limit

Q: Express the limit as a definite integral. lim 40 E xk A xk; [-5, 1] k=1 1 9x8 dx -5 x9 dx x9 dx x dx

A:

Q: lim b-> -0.1x e 1.

A: Let I=limb→∞∫1be-0.1xdx

Q: > If f is a continuous, decreasing function over [1,0) and the lim f (x)=0, X00 then :)dx is…

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: Find the limits limx→q(ln x)1/x

A: Given,     limx→qln x1x

Q: 2. Find the the limit. li -y 1 (tany): 2 Y- 2

A: Given that:                limy→π2-(tan y)π2-y

Q: If f(5)-0, then which of following must be true? fis continuous at x-5 f has a horizontal tangent…

A:

Q: For what value of the constant c is the function f continuous on (-o, 0)? cx2 + 3x if x < 2 f(x) =…

A:

Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

A:

Q: Find the limit of the transcendental function. lim e-2x sin Ax X→0

A: NOTE: Refresh your page if you can't see any equations. .

Q: 7. Because of their connection with secant lines, tangents, and instantaneous rates, limits of the…

A: Answer

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: (-cx² + 2x, (sin x + cos x, x> n x<π 9) Prove that lim (x* sin+5) = 5 10) f(x) = What value must c…

A:

Q: Question 3 (a) Show that the limit łycosy lim (x.y)→(0,0) 2x4 +y² does not exist.

A:

Q: 15) Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated…

A: Given I(t) = t2+3.5t+48    (1 ≤ t ≤ 9)E(t) = 0.5t2−1.4t+13    (0 ≤ t ≤ 10)

Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

A:

Q: If ƒ' is continuous on [0, ∞) and lim→∞ f(x) = 0, show that I p'(x) dx = = -f(0)

A: First we will integrate then put limit

Q: Estimate the limit numerically or state that the limit does not exist (DNE): lim x→0 sin(11x)/x

A: Evaluating the limit

Q: 4x 24. lim x→1/4 tan x

A:

Q: Find the limit. lim est - 1 t-0 sin(t)

A:

Q: d. lim x²(ln x)² x→0+ e. lim (cos x)'1/x X→0

A:

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

A: Given,

Q: Find the limits limx→0+x (ln x)2

A: Consider : limx→0+x(ln2x). Modify the limit function. limx→0+(ln2x)1x…

Q: Find the limit. est - 1 lim t-0 sin(t)

A:

Q: You may assume that the sine and cosine functions are continuous and may freely use techniques from…

A: (a).   We have to find the limit of:   limx→0 sin(2x)-2xx3

Q: x sinh x 1. lim x0 cos 3x -1

A: The solution of the problem is given in the next step.

Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

A:

Q: -7x2 – 6x + 1 x<0 x 20 f(x) = 3 sin x Enter DNE if the limit does not exist. lim f(x) = 1 lim f(x) =…

A:

Q: f(x) lim sin(5x) X I 0 -0.25 3 2 Estimate the limit numerically or state that the limit does not…

A: We have to find out limit

Q: Find the limit: 1 – cos(x) lim x2

A:

Q: The graph of a function f and its tangent line at 0 are shown. What is the value of lim X→0 e7x f(x)…

A:

Q: find the limit as x goes to infinity of ln(x+1/x+2)

A: Evaluate the limit

Q: Find the limit. lim X→- 47 Vx+ 15 cos (x+ 4x)

A:

Q: Find the limit sin(3x)cos(4x) lim→0 x+xcos(5x)

A:

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: 6 - x - x² if x ≤ 1 if x > 1 2x - 9 Calculate the following limits. Enter "DNE" if the limit does…

A: f(x)=  6-x-x2    if x≤1 2x-9         if  x&gt;1

Q: Find the limit. cos(x) – 1 +x² .2 lim 2x4

A: NOTE: Refresh your page if you can't see any equations. . apply L'Hopital's rule

Q: Find the limit. (e-2x cos(x) lim

A:

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.