3) Fuid lhe limit of tihe follaming qunctions: 1as luin (X)→()(2+すり

Q: Evaluate the limit using L’Hôpital’s Rule

A:

Q: Tim (X-1)sec(Tix/z) X -

A:

Q: Evaluate the limit using L'Hôpital's rule e" + 2а — 1 lim 3x

A:

Q: if r = -1 Is f(r) = · continuous at r= - -1? (Show your work using limits.)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: tanh r 4. lim -40+ secha - 1

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Show that the limit does not exist. (x + y)² lim (7,y)→(0,0) x² + y²

A: We have to check

Q: 2. x- 4 lim tan(rx)

A:

Q: 4 – 3" lim,40 -

A: Evalute this limit  problem lim(x tands to 0 ) (4x -3x )/(x). Here i attached solution of this…

Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x,y)→(0,0) x²+y2

A: To show that the limit of a multivariable function does not exist,…

Q: Evaluate the limit with either L'Hôpital's rule or previously learned methods. 5t In(t) lim t- o 8 +…

A:

Q: Show that the following limit ry lim (.v)-(0,0) 22 +y? does not exist.

A: Substitute y=mx, and check by applying limit.

Q: What go in the blank as limit approaches 0:

A:

Q: Show that the absolute-value function y = abs(x) = |x| is NOT differentiable at x = 0. (Hint: by…

A:

Q: Evaluate the limit using L'Hospital's rule 8* – 3* lim X+0

A:

Q: Evaluate the limit using L’Hôpital’s Rule

A:

Q: Use the definition of limit to prove lim (r+ 4y²) = 6. (2,y) (2,1)

A:

Q: Evaluate the limit using L'Hôpital's rule. limx→0  ex+2x−1/9x

A:

Q: Evaluate the limit using L'Hospital's rule: x13* lim x→0 13* – 1 -

A:

Q: limit as x----0 for the function (px)/(sqrt(bx+a^2))-a using L'Hopitals

A: Apply the limit.

Q: Explain why the paths y = mx and x = y² are suitable to check if the limit of f(x,y) = as (x, y) →…

A: *This question belongs to several variable (BSc problem) so I am solving it in Advanced math. *

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

A:

Q: lim Z-y)-(0,0) z4+y?

A: To determine the limits of a multivariate function , Convert the limits into one variable and then…

Q: By considering different paths, show that the limit doesn’t exist. lim (x,y)→(0,0) x2yey/ x4+4y2

A:

Q: 2. Compute xe" da using a limit.

A: The given which we have to find the integration from 0 to ♾️  f(x) = xex

Q: (4) Find the limit by interpretting the limit as as an appropriate derivative. (DO NOT USE…

A:

Q: lim r3/2 sin (1/x)

A:

Q: 1) Show that the limit doesn't exists : 3x2 y lim (x,y)-(0,0) x2 + y2

A:

Q: x² - y? lim ) - (0, 0) х? + у? y

A: Here we have to show that, lim(x,y)→(0,0) x2-y2x2+y2

Q: By using the precise definition of the limit of a function show that lim (x,y)→(0,0) 3xy2 /(2x2+ y2…

A: If value of a function at some point is in indeterminate form then we use concept of limit to find…

Q: Show that the limit doesn't exis 3x2 1) (x,y)→(0,0) x² + y² lim 2) (х,у

A:

Q: By considering different paths, show that the limit doesn’t exist. lim (x,y)→(0,0) xy4/ x2+y8

A: Answer

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

A: Given,            limx→∞x e-x

Q: lim x3 In(x) X→0+ to

A:

Q: By considering different paths, show that the limit doesn’t exist. lim (x,y)→(0,0) xy cos y/ 3x2+y2

A: Answer

Q: Evaluate the limit using L'Hospital's rule.    limit of 4cos(3x)sec(-7x)  as x approaches pi/2

A:

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

A:

Q: Evaluate the limit tan 5z lim I0 sin 2z

A:

Q: Estimate the limit numerically. x² lim x+4 O diverges to +o 00 O diverges to -∞

A: Given

Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

A: To evaluate the given limit .

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

A:

Q: 4. Use the € & definition of limit to show that lim (2z+3i) = 2 + 5i. z+1+i

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: sin(2x) 1) lim

A:

Q: Let f(x) 2.x – 5 if x > 5 --- Calculate the following limits. Enter "DNE" if the limit does not…

A: Here we have, f(x)=10-x-x2 if x≤52x-5         if x>5 We have to calculate,…

Q: Estimate the limit numerically or state that the limit doesn't exist: sec (2) lim (Enter DNE if the…

A: To estimate the limit of the given function at x->1+ . Since the given function is continuous in…

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

A:

Q: Q1:Find the limit using L Hopital rule In (csc x) lim xT/2 (x – (1/2))²

A: Given limx→π2ln(cscx)(x-π/2)2 We have to find limit by using L Hospital rule L'Hospital's Rule…

Q: Evaluate the limit using L'Hôpital's Rule. 3x lim x0 sin(x) - x→0 — х

A: From the given limit: limx→03x3sinx-x Now solve: limx→03x3sinx-x=303sin0-0=00    ....indeterminate…

Q: 1. Use the limit definition to evaluate ,(2 – 3x)dx.

A: The given integral is ∫-122-3xdx

Q: Evaluate the limit using L'Hospital's rule 1 - 10x lim 10xe -

A: Given query is to find the value of the limit.

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: