) Find the value of k that makes function continuous at ¤ =4 f(x) = { | 2x +7 > 4 6x -k < 4 (i) If lim f(x) = 18 and lim g(x) = 27 then find lim[3f(x) + 6g(x)] %3D %3D Sæ – e3z I<0 ( ii) Determine whether the function f(x) = is continuous at = 0. 3x – 1 -

Q: If x- 2 1 lim -2 f(x) – f(2) then, the slope of the tangent line at the point (2, f(2)) is m =7. %3D…

A: By limit defination of f'(x) at point x= a

Q: (5х-4, E If f(x) = 0<x <1 show that lim f(x) exists. %3D 4x - 3x, 1<x<2

A:

Q: 6- Follow the graphing strategy and analyze the function f(x)= 3x³ -10x³ State all the pertinent…

A: We have to graph the given function and also find the limits.

Q: The limit of the function lim (-1)Inxis x-0 a b C d 1 11

A:

Q: F(x) = {e^ X-3 OLX Find lim F(x) x 70 im f(x) x 70

A:

Q: Lm x+h -区 メ+h -x , h#o.

A:

Q: 3* Evaluate (a) lim sin y and (b) lim y x-1 Vx +5

A: we have to evaluate the following: a)  limy→π3 siny b) limx→-13xx+5

Q: (-ト-c)s x-5

A:

Q: Find the value of lim f(x) 1 f(x)3= 1+5/x -0.6 -0.5 0.16 01 E -0.6

A: To find out the correct answer.

Q: Find lim f(x) if f (x) = 3Vx + 2 x 2 %3D X-2 Determine the intervals where the function given in…

A: Given f(x=3x+2x&lt;2x2+2x≥2

Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: ketch by hand the graph of a function f that satisfies: (a) f(2) = 3 and )lim,-+2 f (x) = 4. Is the…

A: Given:   Limit equations is given

Q: 13. Sketch the graph of f (x) = }" Sx² + 1 if x -1 and use it to evaluate lim_ ƒ (x) and X→-1- lim…

A: Given that: f(x)=x2+1    if    x≤-13            if     x&gt;-1

Q: tan3x 6. lim X-0 tan4x

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

Q: : State the three-part Definition of Continuity.

A:

Q: S 1.4x + 0.8, x -2 f(-2) = lim f(x) = x--2- lim f(x) = x--2+ lim f(x) = || x--2

A: E

Q: I +b if x > 2 2) Suppose f(x) ={a if x = 2 if r < 2. (a) Find the value of b if lim f(x) exists. (b)…

A: Solution

Q: Find lim f (x) if, for all x, 9 cos (4x) <f (x) < 8x2 +9. lim f (x) = %3D

A: The given inequality is: 9 cos(4x)≤f(x)≤8x2+9

Q: (3х + 3с if x >2 Let f(x) = {x2 - cx if x < 2 If lim f (x) exists, find the value of c. X-2

A: Limit of a function exist , when both sided LHL and RHL exist.

Q: If f(x) = x² then lim f(x) – f(2) = 0 . x – 2

A:

Q: Find the limits

A: we have to find the limit : limx→∞x+sinx+2xx+sinx

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.