Let ƒ(x) = (x2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01, -3.001, and so on as far as your calculator can go. Then estimate limx--> -3 ƒ(x). What estimate do you arrive at if you evaluate ƒ at x = -2.9, -2.99, -2.999,...... instead? b. Support your conclusions in part (a) by graphing ƒ near c = -3 and using Zoom and Trace to estimate y-values on the graph as x -->-3.

Q: If x3 f(x) s x for x in [-1,1], find lim f(x) if it exists. X-0

A:

Q: Find the value of -1 tan (5x) lim- X

A:

Q: Consider limx-4 f(x), where f(x) 14x+ 9. Find a maximum value of 6 such that: If(x) 65< 0.006 if |x…

A: Plug f(x)=14x+9 in the given inequality and simplify.

Q: Find the limit. lim etan x x-(1/2)+

A: 0 is answer

Q: Let ƒ(x) = (x^2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01,…

A: Consider the given function:

Q: Find lim f(x) for the given piecewise function. X6 2x + 1 if x 6 If the limit does not exist, enter…

A:

Q: Show that lim,→»(1+ e* for any x > 0.

A: To prove:

Q: Evaluate lim as x approaches negative infinity 3e^2x + 4e^-x / e^2x - 2e^-x .

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

Q: Find the indicated limit. 2x lim (- Vx2+1 X00

A: Find the indicated limitlimx→∞(2xx2+1)

Q: ; Be h(x) = - 2x + 1, x + 3 calculate lim h(x) 7,x = 3 x-3

A:

Q: Let f(x) = x/(x + 1). What is lim, »f(x)? How large does x have to be so that f(x) > 0.99?

A: Given:            fx=xx+1 Find: limx→∞fx=limx→∞xx+1

Q: Find the limit: Vx – 14 lim x → 196 196 - Give an exact answer or keep at least three decimal…

A:

Q: Find the limit, if it exists. 2. lim X - 00 4x + sin x

A:

Q: Estimate the value of lim 1 + 3x 1 by graphing the function f(x) = x/(/I + 3x – 1).

A: It is given that limx→0x1+3x-1 It is known that if we have limx→af(x)g(x), and after plugging the…

Q: Let F(x) = (x2 + 3x + 2)/(2 - | x | ). Make tables of values of F at values of x that approach c =…

A: Given: Fx=x2+3x+22-x To determine: We have to estimate limx→-2Fx by making a table of values of F at…

Q: If you know in advance that lim f (x) exists, can you determine its X+5 value from a plot of ƒ for…

A: Given that limit of f(x) exists at x=5.That means the function f(x) is continuous and differentiable…

Q: a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x5 f(x) exists.

A: solution is given below..

Q: Find the indicated limit 2x lim( Vx +1 10)

A:

Q: Find the Limiti lim (xt +2x") メ→ -○

A: Solution is given below

Q: Evalute the lim sin5x/x(x-1) as x approaches 0.

A:

Q: If f (x) = −x + 8 for x ≤0 and f (x) = 4x + 7 for x > 0, find (a) limx→0+ f (x) (b) limx→0− f (x)

A: We can find the limit as below.

Q: Estimate the limit numerically. x+14x + 49 lim x+7

A:

Q: In a model of the nervous system, the intensity of excitation of a nerve pathway is given by I = E[1…

A: Given  that: I=E1-e-a(S-h)E

Q: Estimate the value of the limit lim, 4 x² + 1 by filling out this table and then making an educated…

A:

Q: Find the indicated if it exists: lim x to +infinity;  2x2+3x+1 divided by x4 - x2

A:

Q: Let ƒ(x) = (x2 - 9)/(x + 3). Make a table of the values of ƒ at the points x = -3.1,-3.01, -3.001,…

A: Given, fx=x2-9x+3   x=-3.1 x=-3.01 x=-3.001 x=-3.0001 x=-3.00001 fx=x2-9x+3 -6.1 -6.01 -6.001…

Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1…

A: Make tables of the values of ƒ at values of x .

Q: lim (In 2x + 5) + 4 X→ー1

A: Solution:limx→-1ln2x+5+4=ln2-1+5+4

Q: Show that the function given below is continuous. 4v2 - 16v lim -2 v-4

A:

Q: lim (-2 xS t x-1)

A: From this limit, we know that when x approaches -infinity then y approaches +infinity. so, on the…

Q: Find limx∞ h(x), if it exists, f(x) = 5x3 − 3…

A: Given: fx=5x3-3

Q: B) By using (A), Find lim /-

A: limn→∞1n

Q: . What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

A:

Q: Find the limits of the functions below a) limx-3 x* sin x b) lim,

A: We can find the limit of both the question as below.

Q: Use l’Hospital's Rule to show that lim 1+ X. = e. コ

A:

Q: 1. If V5 - 2x² s f(x) s V5- x? for -1sxS1, find lim,-o f(x).

A: Answer and explanation is given below...

Q: a. Graph h(x) = x2 cos (1/x3) to estimate limx--&gt;0 h(x), zooming in on the origin as necessary.…

A:

Q: The function f(x) of the below graph is discontinuous at x = -1 because: a) f(-1) does not exist b)…

A:

Q: Estimate 1/1−2^1/x from the graph limx→0+

A:

Q: Find the limit of the function algebraically. x2 + 2x lim

A:

Q: Consider the function…

A: The graph of f is as follows:

Q: a) By graphing the function f(x)=(cos2x-cosx)/x2 and zooming in toward the point where the…

A: Graph: f(x)=cos(2x)-cos xx2f(x)=cos2x-sin2x-cos xx2

Q: Determine a reasonable estimate for lim hx x-1 3 -5 -4 -3 -1 3 5 2. 1 4. 1. 1. 2. ee

A:

Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: Find the limit using your understanding of the end behavior of the function. lim e* 7x

A:

Q: 2f(x) + 3x – х — 1 15 - Suppose that lim 5. Find lim f(x).|

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.