evaluate the limit using continuity. (x² + y) lim (х,у)->(1,2)

Q: Find the limit lim Vz +1 Enter I for o0, -I for-oo, and DNE if the limit does not exist. Answer

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Q: Determine if the pointwise limit lim_(n→∞)(ex/n/n) for x ∈ R is uniform. If yes, is the limit…

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Q: Calculate the limit and show proof if it does not exist. lim (r,9)(0,0) (x2 + 2y6)2

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Q: Use limit laws and continuity properties to evaluate the limit. 7x+8y lim (x,y)→(0,0)sin y-7 i

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Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

A: Let us start solving the problem step by step and find its limit

Q: Find the limit (if it exists) of A"x, as n approaches infinity, where and x, = a

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Q: evaluate the limit using continuity lim(x,y)→(1,2)(x2 + y)

A: Evaluate the limit using continuity    lim  x,y→1,2x2+y

Q: Find the limit and discuss the continuity of the function.

A: The function is given as,

Q: Evaluate the limit using a definite integral 2 lim n n 1+

A: Let x = i/n Hence, dx = 1/n when i = 1; x = 1/n; As n tends to infinity, 1/n tends to zero. Hence,…

Q: Find the limit L. Then use the - definition to prove that the limit is L.

A: We have given;

Q: Prove that lim (x,y)(0,0) x² + y² does not exist by considering the limit along the x-axis.

A: Given: lim(x, y)→(0,0)xx2+y2

Q: Estimate the limit numerically or state that the limit doesn't exist lim  h→0   5^h−1/h=

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Q: Determine the value of the limit if it exists. If it does not exist, explain why. ry? lim…

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Q: Find the limit L. Then use the - definition to prove that the limit is L

A: Given: limx→0x3

Q: 2. Use the paths x = y and x = 0 to verify the limit. lim (x.y)-(0,0) x2+y²,

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Q: If the limit lim (x,y)→(0,0) F(x, y) = 0 along the path of the form y = kx for any real number k…

A: Follow next step

Q: Find the limit and discuss the continuity of the function.

A: Evaluate lim(x,y)→(2,4)x+yx2+1

Q: 2ry? does not exist. now that the limit lim (z,y)+(0,0) x² + y!

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Q: evaluate the limit using continuity lim(x,y)→(−2,1)2x2/4x + y

A: To evaluate lim(x,y)→(-2,1)2x24x+y

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: evaluate the limit using continuity. lim (x,y)→(1,1) x+y

A: limx,y→1,1ex2-e-y2x+y

Q: Evaluate the limit if it exists, or show that it doesn't exist: xyz lim (a7,1,2)¬(0,0,0) [ æ² + y² +…

A: Evaluate the limit lim(x,y,z)→(0,0,0)xyzx2+y2+z2=0·0·002·02·02=00

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: Find the limit L. Then use the - definition to prove that the limit is L.

A: Consider the following limit: L=limx→21-x2=1-22=1-4=-3

Q: Find the limit if it exists, or show that it does not exist. lim (z.v)-¬(0,0) xª + 4y²

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Q: 2. Use the definition of the limit to prove that lim (r+2y – 1) = 1. (1,9)¬(0,1)

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Q: lim x3 In(x) X→0+ to

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Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

A: Use rules of limit

Q: Use the definition of the limit of a function of two variables to verify the limit.

A: We have to verify the limit: limx, y→1, 0x=1 According to limit value, x, y→1, 0 therefore, x=1y=0

Q: Q1/ (a) By using the definition of limit, prove that lim (3x+iy)=9i. z31

A: Please find the  attachment for the details solution

Q: Find the limit by rewriting the fraction first. x- y + 5/x - 5Vy lim Vx - Vy (ху) -- (0,0) x#y x- y…

A: limx,y→0,0x-y+5x-5yx-y =limx,y→0,0x-yx+y+5x-5yx-y =limx,y→0,0x-yx+y+5x-yx-y

Q: Prove the limit. Using the precise definition of a limit. lim x approaches 0 xsinx(1/x)=0

A: To prove:

Q: Find the limit. lim (х, у) > (1, 55) Vx + у Discuss the continuity of the function. continuous for x…

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Q: If it exists, find Answer: x³ - ze²y lim (x,y,z) (-1,0,4) 6x + 2y3z' Write DNE, if the limit does…

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Q: xy lim 2 (x,y) (0,0) x² + y²

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Q: Compute the limit or state that it does not exist. (If an answer does not exist, enter DNE.) lim (x,…

A: We can compute limit value only when it forms an Indeterminate form while putting limit. There are 7…

Q: 2. Find the limit using Squeeze theorem 1 lim-2|x – 2| sin( r - 2

A: Squeeze Theorem- Let f, g and h be functions defined on an interval I. Let c∈I be its limit point.…

Q: Evaluate the limit if it exists, or show that it doesn't exist: xyz lim (x,y,z)→(0,0,0) [x² + y² +…

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Q: Compute the limit, or show that it does not exist: xy + xy? lim (x,y)→(0,0) x² + y²

A: Given a limit : lim(x,y)→(0,0)  xy+xy2x2+y2 We need to find the limit if it exists or show that the…

Q: x - y + 2Vx – 2/y lim (xy)-(0,0) y+x 'y

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Q: xy? lim (x,y)→(0,0) x² + 2y4 Compute the limit

A: Given limit,

Q: Find the limit if it exists, or show that it does not exist. lim (7,v)>(0,0) xª + 4y²

A: According to the given information, it is required to find the limit of the given function.

Q: . lim,0+ (1 + 2x)In(2z)

A: Solution :1∞  formif limx→0fx=1 limx→0gx=∞if the form limx→0 fxgx then elimx→0 fx-1gx

Q: Evaluate the limit below. 1 lim (x,y)→(0,0) 1-x2-y?

A: limx, y→0, 011-x2-y2

Q: Use continuity to evaluate the limit. e lim (x,y)→(-4,–4) x + y

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Q: 2. Find the limit using Squeeze theorem 1 lim,2|a – 2| sin( `x – 2

A: Given: limx→2x-2sin1x-2

Q: 4. Use continuity to evahuate the limit. 5+ V lim X4 V5+x b) lim e-x X-1

A: