Evaluate, use L'Hopital's rule when appropriate:   lim  (eax+x)1/x x->0                          for a constant a   Thanks!

Q: tan 3x lim x→0 \ e2x – 1 3/2 O 1/2 O 2 O 2/3

A: Solution:GivenTo find the limit oflimx→0 tan 3xe2x-1=?Formula:ddxeax=aeaxddx tan ax=asec2 ax

Q: Now, use direct substitution. 1 lim X-2 x + 7 + 3) = 1/6 Thus, the value of the limit X + 7 lim X -…

A: limx->21x+7+3Directy substitute 2 for xlimx->212+7+3 13+316

Q: What is lim1 f (x) ? X

A: Find your answer below

Q: lim 1 + X00

A: Let, L=limx→∞1+1xxlnL=limx→∞ln1+1xx⇒lnL=lim x x→∞ln1+1x

Q: Find the limits in Exercise

A: To find the limit of

Q: Find the limits in Exercise

A: If we have a function what says limx→c+f(x), this means that the value of x approaches c from the…

Q: Evaluate the limit. limx→(π/2)− (x − π/2)tan x Just letting you know the negative sign is…

A: the given limit,limx→π2-x-π2 tanx

Q: Can the Quotient Law be applied to evaluate lim sin x -? Explain. x+0 X

A:

Q: Evaluate limx-->2 (sin(x-2))/(x^2+4x-12) Without L'Hospital's rule.

A: limx-->2 (sin(x-2))/(x^2+4x-12)Numerator = sin(x-2)Denominator = x2 + 4x - 12 = x2 +6x - 2x - 12…

Q: use L'HOSpital's rule ro show that lim 2tanx イ→ % rc 2x

A: We have to proof

Q: Vx +1-1 2. lim

A: we have to find limit

Q: 2. Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths…

A: A number L is said to be the limit of a function f(x,y) as (x,y)→a,b , if for any real number ∈>0…

Q: lim Vx +x+1 x- - X-∞

A:

Q: Use a tble of functional values to evaluate: lim x-1

A:

Q: Transform the function lim x+5x² +3- x²) into an equivalent quotients to en apply L'hopital's rule.

A: Given that limx→∞x4+5x2+3−x2. Multiply x4+5x2+3+x2 by numerator and denominator both…

Q: What is lim ? X-0+ x

A:

Q: Show the steps needed to evaluate lim(1+ )". Use L'Hospital's Rule.

A:

Q: Find limx→−∞(x2 −1)e4x. Show work.

A: We need to find : limx→-∞(x2-1)e4x

Q: find the limit or explain why it does not exist.

A: To find the limit  limx→π sec x = ?

Q: 2 lim x→1- x²

A: The limit of the function f(x) is obtained as L=limx→a-f(x)L'=limx→a+f(x) Then the limit of the…

Q: Find the limit is it exisit.

A:

Q: Find the one sided limit, lim-0

A: We solve the limit.

Q: Find the limit. If you L'Hopitals Rule, make sure to justify why you can use i use lim 2?e

A: We have to find the limit.

Q: Let fx) = mx + b where m and b are constants. If lim fx) = 1 and lim Ax) = -1, determine m and b.

A: Given: fx=mx+b And limx→2fx=1 and limx→3fx=-1

Q: Evaluate limx-->0 (sin^2 2x)/(2x) Without using L'Hospital's rule.

A: The given funtion is (sin^2(2x))/2x for the limit x tends to 0.

Q: Use I'hospials rule to fidy value lim (4“ +7*)= X¬00

A: Please see the explanation below

Q: Use a table of values to estimate the value of the limit. If you have a graphing device, use it to…

A:

Q: Find lim_f(x), if it exists. If it does not exist, explain why. X--4"

A: Follow the procedure given below.

Q: find the limit or explain why it does not exist

A:

Q: sec(x) – sec(a) lim x - a

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Consider the function f(x) = √x.  Is limx 0 √x = 0 a true statement? Explain.

A: Given: The function f(x)=x Statement limx→0 x=0 We have to determine the given statement is true or…

Q: Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths in…

A: We have to explain why fx,y must approach a unique L as x,y approachesa,b along all paths in the…

Q: ах Determine the values of a and b such that lim Vax +b – 3 = 5. x→0 bx

A:

Q: Find the follow ing limits. lim ex -|-X メラ0 セメーーメ ィス

A:

Q: Find the limit (if it exists). If it does not exist, explain why.

A:

Q: lim x→め x th

A: Let L=limx→∞4+x2x

Q: Which property of f(x) = x' allows us to conclude that lim x- 8?

A: f(x)=x3 is a continuous function. So, it is continuous at x=2 also.

Q: Find the limits. If you use L'Hopitals Rule, make sure to justify why you can use it. 1- cos(2r) lim

A: To find the limit- limx→01-cos(2x)x2

Q: evaluate using Theorem 2 as necessary.

A: We rewrite the given expression as:

Q: Q1. Using Lopital Rule ,Find :lim -cos

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: use f(x) to find: limx→0f(x), limx→-4f(x), limx→5+f(x), limx→-4-f(x). the discontinuity that is…

A:

Q: By using Sandwich Theorem, prove that lim sin r X-0 x

A:

Q: Lim xsinx

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

Q: By using Sandwich Theorem, prove that lim sin x

A:

Q: lim (Vx2 + 4x + x)

A:

Q: Find the limits limx→∞csc-1 x

A: Given:limx→∞ csc-1x

Q: 3 – Vr +7 it lim х — 2

A:

Q: Calculate the limit for the given function and interval. Verify your answer by using geometry.

A:

Q: Find the limits. Are the functions continuous at thepoint being approached? lim x →π sin (x - sin 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.