If function f(x) and g(x) are continuous everywhere and f(1)=2, f(3)= -4, f(4)=8, g(0)=4, g(3)= -6, and g(7)=0 then limit of (f+g)(x) as x approaches 3 is equal to * О 10 O 11 O cannot find a value for the above limit since only values of the funtions are given

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A:

Q: Use L 'Hopital 's Rule to evaluate the limit.

A:

Q: 1) Show that the limit doesn't exist 3x2 1) (x.y)(0,0) x2 + y² lim 2) (x.y 3) lim ysinx 4) lim

A:

Q: limit

A:

Q: 2. Evaluate the limit: TC 1000 lim x-7- (x-7)2 lim x→8+ (8 - x)3

A: the given limit is: limx→7-πx-72-limx→8+10008-x3 we have to evaluate the given limit.

Q: 1. What is the difference between a function whose limit does not exist and one that increases…

A: Definition of Limit: Let E⊆ R and f:E→R.  Let a∈R be such that ((a-r,a+r)    {a})∩E is non empty for…

Q: Show with the epsilon delta definition that the limit when x --> 4 of (x^3-8x^2+16x+4) = 4

A: we have to show with the epsilon delta definition that the limit when x→4 of x3-8x2+16x+4=4 as we…

Q: lim (sec x-tan x)

A: Given: limx→3π2- sec(x)-tan(x)  Compute the limit analytically.

Q: 34. Show that the Product Law cannot be used to evaluate the limit lim (x - ) tan x. xx/2

A:

Q: Using L'Hopital's Rule, we have to find the limit of f(1+ x) – f(1 – x) lim xf'(1) |

A: If the Direct substitution will results the answer in the form 00 or ∞∞ then we can use L'Hospital's…

Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim 2 x→1 x´ + x -2

A:

Q: In (x) — х + 1 lim x² 2х + 1 x→1

A:

Q: Give an example of a limit of the form ∞ / ∞ as x→ 0.

A:

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: given find the limit numerically limx→23x−95x−25

Q: Evaluate the limit |x – 4| lim x-4 x- 4 If the limit does not exist enter DNE. Limit =

A: →For existance of limit at any point,         Left hand limit(LHL) and right hand limit(RHL) at that…

Q: How does the sandwich theorem enable us to calculate a variety of limits?

A: Sandwich theorem: Consider 3 function f(x),gx,hx such that fx≤gx≤hx. Also, assume that limx→cf(x)=L…

Q: given that  lim f(x)=9           lim g(x)=-2             lim f(x)=0 x--->1.…

A: Note: We shall only answer up to first three sub-parts as the exact one is not specified. Please…

Q: Find the limit (if it exists). (If the limit does not exist, enter DNE.) - (x² - -/-) lim

A: The given limit limx→0-x2-3x

Q: How many times do you have to apply L'Hopitaľ's rule to evaluate the limit x- sinhx lim x-0 x sinx…

A: Given limx→0x-sinhxxsinx

Q: limf(x) does not care what happens While a limit exactly at x = c because the limit is concerned…

A:

Q: Use different path of approach to the point (0, 0) to show that the limit lim(,9)→(0,0) 4 does not…

A:

Q: Find the limit. lim x--s+ (x + 5)2

A: The given limit,limx→-5+1x+52

Q: limit as x---3 for the function (x-2)^11/(3-x) using L'Hopitals.

A: Consider the given function (x-2)11 / (3-x).

Q: b) Use L'Hopital's rule to find the limit: 1/In x (In xv lim

A:

Q: Compute the limits that exist. lim x---0, x2 + 3x/x

A: Given: limx→0x2+3xx

Q: 4 Find the limit: lim sin(x) (Enter undefined if the limit does not exist.)

A: The given limit limx→04x-4sin(x)

Q: Evaluate the limit |x lim x+6 x - 6 - 6| If the limit does not exist enter DNE. Limit =

A: Evaluate the limit

Q: Choose the limit that would NOT use l'hopital's rule. 1³ – 1 lim I →1 1² – 1 (=* – 1) (=² – 1) * lim…

A: We can find the answer as given below

Q: Evaluate. (a) limit as x goes to 0 -> (tanx)/(2x) (b) limit as x goes to 5 -> (-1)/(x-5)2 (c)…

A: a) The limit can be evaluated as.

Q: In(1+ x?) lim x-0 x3

A:

Q: 2. Use limits to describe the types of discontinuities at x = 1 and x = 3. Justify your work by use…

A: There are a total of 3 discontinuities: Point/Removable Discontinuity, Jump Discontinuity and…

Q: compute limit as x goes to infinity of xe^-x

A: Given,            limx→∞x e-x

Q: If lim f(x) and lim f(x) exist but are not equal, then x = c is a(n) jump discontinuity. X-C- XC+ If…

A:

Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim x→1 x´ +x –2 2

A:

Q: e4x – 1- 4x lim x2

A: topic - limit using l 'hospital rule

Q: Actually the range of possible results for a limit with a 00 indeterminate form is anywhere from 0…

A: Example of a limit with the form 00 is provided.

Q: Vx+14-4 Compute the limit analytically without L'hopital's rule: lim X-2

A: Given limit is : limx→∞x+14-4x-2 To find the value of limit.

Q: 5) Prove that the order of iteration of limits can be significant by showing that х2 lim(lim у-0…

A: It is needed to prove that order of iteration of limits can be significant by showing that:

Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hôpital's Rule. sin(2x) lim 5x…

A: Limit: a)    x→0limsin (2x)5x=x→0limsin (2x)2x*52=25x→0limsin(2x)(2x)=25.1=25We know ,…

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

A:

Q: x2 + 2x + 1 lim x--2 x2 + x +1

A: There is no need for L hospital as the limit can be evaluated directly.

Q: How many times do you have to apply L'Hopital's rule to evaluate the limit x" lim k<0 if n=9 Select…

A: Given that limx→∞xnekx, k&lt;0. We have to check how many times we can apply L'hospital rule to…

Q: limit as x approaches infinity of (-1)x+1

A: Apply the limit.

Q: Alice and Bob are trying to compute lim x→∞ of cos(x)/x   Both of them know that they only have to…

A: We know that the range of cosx is [-1, 1]. Therefore Therefore Alice is correct. Now,

Q: 7. Show that the limit does not exist by approaching (0,0) lim .2 ,2 + y- (x, y) (0,0)

A:

Q: If lim 2 4xk (1-3xk)Axk,a= - 3,b=3 Then the correct expression for the limit as integral is: k =1…

A: Let's find.

Q: 2. Evaluate the limit by Use the definition of the derviative to compute the derivative of f(x) = 1…

A: Given,

Q: Express the limit as an integral. Š (5(x; )² – 3(x; )³)ax over [0, 2] lim

A:

Q: 8. Find the limit using squeeze theorm. lim x² sin(x²)

A: