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

Q: Jse the two-path test to prove that the following limit does not exist. y* - 2x? lim 4 (x.y)-(0,0)…

A: Since tha value of both the limit is different  Hence the limit does not exist.

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: 2] Show that the limit does not exist by considering the limits as (x, y) → (0, 0) along the…

A:

Q: lim (x² + 1) = L x→2

A: Topic:- calculus

Q: 1. Determine whether or not the following limit exists. Be sure to include an argument supporting…

A: Given limit function: limx,y→0,02x2-xy-y2x2-y2 First, trying to solve by direct substitution,…

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: 2) Find the limit if it exists. (ху — Зх — у + 3)(2? — 4z + 4) (х — 1)4 + (у — 3)4 | | | lim…

A: We have to solve given problem:

Q: Suppose that f: R→R is a continuous function, satisfying f(5)=8. What is the value of the limit lim…

A:

Q: Find the limits as x 0 and as x→ -o. (If the limit is infinite, enter 'oo' or '-0', as appropriate.…

A:

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

A: The statement of continuity states that if f(x) is continuous, then f(a)=limx→af(x), where a is any…

Q: 3. Use continuity to evaluate the limit. (5 – x2 lim In x+1 1+ x

A: We have to find limit

Q: (a) Show that the limit x*ycosy lim 12 (xy)→(0.0) 2x* +y² does not exist.

A: Student has specifically asked for the solution to question (a).

Q: Find the limit. 11ry lim (2, y) (0,0) x2 + y? The limit is O The limit does not exist.

A: For a two-variable function, its limit as (x,y)→(a,b) will exist if and only if the limit…

Q: 4. Find the limit, if it exists or show the limit does not exist: a) lim (x,y) (0,0) x + y* .2…

A:

Q: 8. Using squeeze theorem, show that the following limit (x – 1)² In x = 0. lim (x,9)→(1,0) (x – 1)²…

A:

Q: Use limit laws and continuity properties to evaluate the limit. 3x+5y lim i (x.y)-(0,0) sin y+1

A: Explanation of the answer is as follows

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

A:

Q: 2.a?y Using paths, show that the following limit does not exist. lim (x,y)→(0,0) 3x4 + y?

A: According to the given information, it is required to show that limit does not exist.

Q: b) Use the concept of infinite limit to compute the following: (1 – i)z + i lim 2-i/2 2z +i

A: To compute the limit: limz→i21-iz+i2z+i Explanation: The concept of limit states that if the highest…

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

A: limx,y→1,1ex2-e-y2x+y

Q: 2. Evaluate the limit or state that it does not exist: xy – 4y? lim (2,49)→(4,1) Va – 2/y

A:

Q: The limit: x - y lim (x,y)→(0,0) x² + y² exists, and equal to 0 Select one: O True O False

A:

Q: 4 – V* lim x 0 2 + Vx

A:

Q: x² + 2y? + 3z² 18. lim (x, y, 2) →(0, 0, 0) x² + y² + z?

A: We have to find the limit by two ways method

Q: 5 42sin(t®)dt Evaluate the limit lim

A: the given limit is: limx→0∫0x42sint6 dtx7 we have to evaluate the given limit. limx→0∫0x42sint6…

Q: The limit lim (x c 1 X• COS is an indeterminate form of type 0· o. Select one: True O False

A: Given: limx→∞x·cos1x   As we know that; limx→afx·gx=limx→afx·limx→agx

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: 2. Evaluate the following limit. 2хy? lim (x,y)-(2,1) 3x² + y2

A:

Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. 22 - 7x + 6…

A:

Q: cz+ 2) Use the definition of limit t. prove; lim 2=4 22

A:

Q: Find the limit lim (|z|² - iz) Z→1-i

A:

Q: The limit: does not exist Select one: O True O False x² - y² lim (z,y) (0,0) 4x + 4y

A:

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: 1. Evaluate the limit: xy - y lim (x, y) → (1, 2) x² - x+2xy - 2y

A:

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

A:

Q: 2.Find the indicated limit or state that is does not exist x* – y* C. lim (x,y)→(0,0) x² +y ху d.…

A: Solving

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: 5. Use a table of values to estimate the value of the limit. a). f(x) = lim x² -3x est –1 b). f(t) =…

A: Gg

Q: Show that the limit does not exist. xy? lim (x,y)→(0,0) x3 + y6

A:

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

A:

Q: The limit lim sin x does not exist. O True O False

A:

Q: 2. Determine the value of the following limit along all paths through the origin for which x + -2y.…

A:

Q: 1. Find the indicated limit or state that is does not exist lim (3x'y- xy³) а. (x,y)→(1,3) b.…

A:

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

A: Given: limx→2x-2sin1x-2

Q: 6. Find the limit lim Enter I for o0, I for-oxo, and DNE if the limit does not exist, Answer

A:

Q: Xy Using the definition of limit (e - 8) to prove that lim (x, y)→(0, 0) 2x² +3 y = 0.

A:

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: