Determine whether the function u below has a limit as x 0o. If it has a limit, find it. u : R0 → R, u(x) = sin(3/x) · In(2æ) lim u(x) %3D Hint: if the limit of the sequence is oo, type: infinity. If the sequence has no limit, type: DNE. Check

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Plug x=4 to find f'(4) Answer: f'(a)= -1/16

Q: Use the figure to find the limit a in the interval [a, 4] such that f (x) dx is smallest. f(x) + 2 3…

A: To solve the following problem

Q: 10. Find the value of the limit or state that it does not exist (DNE). a) lim f(x)= =(x)s u X -3

A: Given

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) x² sin2(y) lim (x, y)→ (0,…

A: To evaluate: lim(x,y)→(0,0)x2sin2(y)x2+8y2

Q: Find the limit. lim e 3t i е j + Sin2 tan(5t) k) t 0

A: The given expression is,

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (e-X + 5 cos(2x)) x- 00

A: Cosine is a period function,it does not approaches any values as x approaches to infinity.

Q: Use a graph to estimate the value of the limit. Then, use l'Hospital's Rule to find the exact value.…

A: Here, I am solving 1st two parts and for the remaining part please post the question again. Part A…

Q: Consider the function In(ay? +1) S(a, y) = %3D (a) Does the limit lim (x. y) - (0,0) exist? If it…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 1 lim t→0 1 + t

A: Given: (a)   (b)

Q: Use the definitions of the hyperbolic functions to find the following limit. lim 8sinhx X+- 0 а. 1…

A: The solution are next step is

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

A: As we know that the limit of a function is valid when both the limit. RHL and LHL are equal.…

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) xy lim (x, y)→ (0, 0) x² +…

A: Given limit is: L=limx,y→0,0xy4x2+y8 Let y = mx.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) sin(9t), lim t-0 e5i +…

A:

Q: lim (x, y)→(0, 0) xy4/x2+y8

A: Given limit  L=limx,y→0,0  xy4x2+y8

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim t-0 eSi + sin(2t). -) +…

A:

Q: Use the graph of the function f to find the limits at the indicated value of a, if the limit exists.…

A: Limit of a function at x=ais said to exist iflimx→a-fx=limx→a+fx

Q: 1- cos?t lim t-0 t

A:

Q: Evaluate , x? dx by limit definition. f(x) dx f(G.) Ax¡ lim i=1

A: Given integral  ∫01x2dx △x=b-an△x=1-0n=1n ci=a+i(△x)ci=0+i1nci= inf(ci)=in2

Q: f(x, y) = e¬aY sin(x + y) (г, у) —> (1, -1). as

A: We will plug the limits in function to find limit of function

Q: Find the limit. (e-4t i + j+ sin(5t) k sin?(t) lim

A: We have to solve given problem:

Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

A:

Q: Find the limit. (Hint: Let x = 1 / t and find the limit as t→0+.)

A:

Q: Evaluate the limit lim (x,y)→(1,1) V(a - 9). sin(x – y) x2 – y? O A. OB. OC. 3 OD. 5 O E.

A: option B is correct

Q: ху? lim xy? cos y (x, y)→(0, 0) x2 + y*

A: limx,y→0,0xy2cosyx2+y4Along…

Q: OF# Usc the L'Hospital's Rule to compute the limits: B) lim x+5 B00 2x+5* A) lim log, (1+ 2x+x?) and…

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y)→(0, 0) (x2 +…

A: Formula used:A function f(x, y) is continuous at the point (a, b) if,

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE 2 2 lim t-0t t2 +t

A:

Q: Determine whether the function u below has a limit as x oo. If it has a limit, find it. u : RSo → R,…

A:

Q: 1. Consider the function given by if r € QU [0, 1] f(x) = 1- I 1 ° if r E Q°U [0, 1] Determine if…

A:

Q: Given that f(x) = e ,which of the following is equal to the limit F(; + h) – f(}). lim h→0 ? h Oe…

A: From definition of derivative we know for a function f(x),  limh→0f(a+h)-f(a)h=f'(a)

Q: Evaluate the limit using L'Hospital's rule e – 1 lim I+0 sin(2x)

A: The given limit is in 0/0 form.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ti+ sin(t)j + cos(t)k)…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 9 lim t-0 1 + t ty

A: Given :limt→0 9t1+t-9t

Q: Find the limit. lim (e-4t i - j+ sin(6t) k sin?(t)

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim xy (x, y) (0, 0) x2 + y8

A:

Q: Find the limit lim (t), where F(t) = (-1 v1+i-1 sin (2t) – In (t + 1) \ 3t 31y Find the limit or…

A:

Q: Please

A:

Q: Q4. Find the limit cos ec (t)-cot (t) lim- t

A: Answer and explanation is given below..

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) x4 – 8y2 lim (x, y) → (0, 0)…

A: Topic :- Limits Answer = Limit DNE

Q: Evaluate the limit using L'Hospital's rule ez – 1 lim z+0 sin(82)

A: Here I have appended the formula used in the solution part.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e³ti+ sin(4t)j + e-6tk…

A:

Q: sin²t t3 lim t-0 sint

A:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) x + y lim (x, y) → (0, 0) x…

A:

Q: c) Find the limit of the following functions by using L'Hopital's Rule. (i) lim (cosec x (ii) ex +…

A: As per our company guidelines we are supposed to answer only first part . Kindly repost other parts…

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)  lim t→0  (1/t) -…

A: Given limt→01t-1t2+t        ⇒limt→01t-1tt+1∵taking 't' common         ⇒limt→0t+1-1tt+1∵ using…

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y) → (3, –3)…

A:

Q: Find the following limit if it exists, or show that the limit does not exist, y? sin? x lim…

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

Q: Let f(x) = {. (4 – x – a? if a 4 2x – 24 Calculate the following limits. Enter "DNE" if the limit…

A:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim_ (ti+ sin(t)j +…

A:

Q: e the squeeze theorem to find the following limit, if

A: