use any method to evaluate the limit or show that it does not exist. lim(x,y)→(0,0)x2 − y2/x2 + y2

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) Vx +5 - V5 lim x-0

A:

Q: Find the limit, if it exists, or show that the limit does not exist. x² - 3y² lim (x,y) (0,0) x² +…

A:

Q: (a) By using the definition of limit, prove that lim (3x+i z31

A: Introduction: Limits in mathematics are distinct real numbers. Consider a real-valued function "f"…

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) x + 1 lim X→3 X - 3

A:

Q: Find the limit, if it exists: X lim X+- 0 x² + 1 ,2

A: We factor out x2 from inside the square root. Then |x| comes out of the square root. Note that: x/…

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) 2 lim X→3+ x + 3

A:

Q: Find the limit, if it exists. (If an answer does not exist, 3 - xy ху lim (x, y) → (2, 1) x² +2 +9y²

A: We will apply the limits.

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

A: A limit limx→afx exists if its both left-hand and right-hand limits are equal and finite. The…

Q: Evaluate the limit, if it exists. If not, determine whether the one-sided limits exist (finite or…

A: Given:

Q: Find the limit or show that it does not exist. V1+4x (1) lim x-o 2-x3 (2) lim (V9x2 – 5x+3x

A:

Q: Evaluate the limit if it exists, or show that it doesn't exist: (x + 3) e"! lim (2,1)(0,1) y+1

A:

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

A: Evaluate lim(x,y)→(2,4)x+yx2+1

Q: Evaluate the limit limx→5 x^2 − 2x −15  /  x−5 Enter I for ∞,  −∞ and DNE if the limit does not…

A: First, we factor the numerator

Q: t2-3t+5 lim -1+ 0 t

A: Given:        limt→0et−1t+t2−3t+5t2−1

Q: Let f(x)=2x2+7f(x)=2x2+7. Evaluate limh→0f(−2+h)−f(−2)h.limh→0f(−2+h)−f(−2)h. (If the limit does…

A: Given function is Firstly, we find f(-2+h) and f(-2) as follows.

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 2 - X lim X→2 Vx + 2 – 2

A:

Q: Use any method to evaluate the limit given the figure below or show that it does not exist

A: Given: limx,y→0,0x2-y2x2+y2

Q: Find the limit, if it exists, or show that it does not exist: x² – y? lim (x,y)→(1,1) x³ – y3 '

A: Explanation of the answer is as follows

Q: Find the limit, if it exists, or show that the limit does not exist: lim (x,y)→(1,-1) 3-xy cos(x +…

A:

Q: Find the limit: ху lim (x,y)→(1,1) x² + y²

A: Apply the limits

Q: Find the limit if it exists. g³ – xy? lim (a) (1,9)→(0,0) x² + y²

A:

Q: Evaluate the limit, if it exists.

A:

Q: Find the limit (If It exists). (If an answer does not exist, enter DNE.) (x² - 4x +18, -x² + 4x -…

A: Put the condition for existence of a limit and cross check.

Q: c- Show that the following limit does not exist (x² - y²) lim (x,y)-(0,0) x2 + y² 2

A: Given ; lim(x, y) -(0,0)[(x2-y2)/(x2+y2)]2.

Q: Show that the limit does not exist: (y² + x – 1)² - lim (x,y)→(1,0) (x – 1)2 + y4

A:

Q: x" x² - y² lim (x,y) (0,0) x² + y² 2

A:

Q: b) Find the limit, if it exists, or show that the limit does not exist. 3x4 - 3y4 lim (x,y) (0,0)…

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) ' 4 - lim t-0\t t2 +

A:

Q: Find the limit, if it exists, or show that the limit does not exist. a) lim (x,y)→(0,0) 3x2+2y2/…

A: (a)-lim(x,y)→(0,0)(3x2+2y2x+1)Put the value (x,y)=(0,0)lim(x,y)→(0,0)(3x2+2y2x+1)=302+2020+1=0…

Q: xy-y lim - y(-1.2) (x + y + 1)

A:

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: 4. lim Vx+3–2 x→1 x-1 5. lim et –e2x 1-er

A:

Q: Evaluate the limit if it exists, or show that it doesn't exist: (x + 3) eay lim (x,y)→(0,1) y + 1

A:

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

A:

Q: Find the limit, if it exists, or show that the limit does not exist. 2 x² - 3y² lim (x,y)→(0,0) x² +…

A:

Q: Find the limit, if it exists, or show that the limit does not exist. 3x²+2y2 2x*y+2 a) lim…

A: now , we will find the limit .

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) x2 - 4x + 18, l-x2 + 4x -…

A: Detailed explanation mentioned below

Q: 9. Find the limit, if it exists. (If an answer does not exist, enter DNE.) Vx²+x a) lim X--00 -3x

A: topic- limits

Q: 2) Show that the limit exists : 3x3 ,3) lim (x.y.z)-(0,0,0) x2 +y² + z2

A:

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

A: To find the limit of the function x2+1 at x = 1   Left hand limit  limx→1- x2 + 1 = (1)2+1 = 2=…

Q: Evaluate the limit, if it exists.

A:

Q: 3. Find the limit, if it exists, or show that the limits does not exist. d) lim (1,y)¬(0,0) xª + y²°

A:

Q: Find Limit Using Squeeze Theorem: 3. If 2x s g(x) s x* – x² + 2 for all x, find lim g(x).

A:

Q: Find the limit, if it exists, or show that the limits does not exist. a) lim (x5 + 4.x³y – 5a²).…

A: Given lim(x,y)→(5,−2)(x5+4x3y−5x2)

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 - 3x + 2 lim X → 2 X…

A: To determine:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) (x2 – 4x + 6, 1-x² + 4x –…

A: Here we find limx→7fx       where fx=-x2+4x-2, x≥7x2-4x+6  x <7if it exist

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: