2. Evaluate the limit using the properties of the limit: 2 7xy lim (x,y)-(2,3) x2 + y2 3. Verify the limit using the definition: 7xy2 lim x,y)-(0,0) χ 2 + y 2 4. Discuss the continuity for: a) g(x,y) x2+y2-9 b) h(x,y)-y-4 a) f(x,y) 4y+x4y2-5xy® 5 5. Find the partial derivatives for: b) f(x,y)-e"cos(xy2) 6. Find the slope in the x-direction and in the y-direction of the surface 2 -x2 +--+-at the point (0,-1,4) using partial derivatives. 4

Q: 2x? +3y2 Let f(x, y) = Set y = mx and show that the resulting ху limit depends on m, and therefore…

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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: The sandwich theorem for functions of two variables states that if g(x,y)< f(x,y)<h(x,y) for all…

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Q: C. Prove that the limit does not exist. 1. lim (xy)-(0,0) x*+3y

A: We need to prove that limit does not exist.Below find the details solution in image.

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

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Q: Let f (r, y) = 5z'y 7+2y0 %3D Evaluate lim)(0,0) f (x, y). Either find the limit or show that the…

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Q: evaluate the limit or determine that it does not exist. lim(z,w)→(−2,1) z4 cos(πw)/ez+w

A: To evaluatelim(z,w)→(-2,1)z4cosπwez+w

Q: 2. Let h(x) = (tan z)". (a) Find the limit lim h(z).

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Q: and If lim f(x) = lim g(x) = +o and flx) =1 and gtxl = e, what is the limit of the division of !!…

A: As given limit is infinitely by infinity form so use L'hopital's rule and substitute the given…

Q: Consider the limit lim (x-1)sin) X-1 X-1 (a) Can this limit be evaluated using substitution? Why or…

A: To evaluate lim(x tends to 1) (x-1) sin[π/(x-1)]

Q: 1.Suppose g and h are functions of two variables such that lim g(x, y) = 10 and Lim h(xy) =5. Prove…

A: Topic- limits

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

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Q: Investigate whether the limit exists lim (r,y)→(0,0) x²y² + (x – y)²

A: Given :                           lim(x,y)→(0,0) x2y2x2y2+(x-y)2  To find :…

Q: Evaluate the limit or determine that it does not exist.

A: Given that limx, y→0, 0 tanx2+y2 tan-11x2+y2. Compute the limit as follows.

Q: Evaluate the limit, or type "DNE" if the limit Does Not Exist: xy lim (2,y) → (1,1) ya

A: We use identity  a2-b2= (a-b)(a+b) use to factories numerator

Q: Let f (x, y) = xy/(x2 + y2). Show that f (x, y) approaches zeroalong the x- and y-axes. Then prove…

A: Given :                     lim(x,y)→(0,0) xyx2+y2          We know that if the limit exist, all…

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: Evaluate the limit lim z→2+i [(z−1)(3−2i)+1−3i] and use the definition of the limit (−δ) to…

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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: 6 Use the e - d definition of a limit to prove e lim 1+2 r2 + 2 1.

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Q: Prove that the following limit does not exist: lim (z,9)(0,0) I-y

A: To Prove: lim(x,y)→(0,0)x+yx-y does not exists   Here, we will check the value of the limit along…

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 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: Q4 (а) Evaluate the limit lim xy cos y if it exist. If not, show that the limit does not (x,y)¬(0,0)…

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Q: Use the definition of the limit ( epsolon - delta ) to show that lim of 1/z as z approaches -i

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Q: Find lim(r,y)→(0,0) ry" Cos y if it exists or show that the limit does not exist:

A: Solution :-

Q: Let f(x, y) = xy /(x 2 + y2). Show that f(x, y) approaches zero along the x- and y-axes. Then prove…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

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: Use the definition of the limit (e – 8) to show that 1 lim - = i. 2+-i z

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

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Q: Show that the limit does not exist. xy? - 1 lim (Ky)→(1,1) y-1

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Q: FInd the limit of the following, or dhow that it does not exist: lim (x,y)-&gt;(0,0)   (2ex tan…

A: Let's call the limit as L. Please see the whiteboard.Between the two variables, first see whose…

Q: Let f(x, y) : and let L = lim( y)>(0,0) f(x, y). Which of the following 9x2 + 3y2 statements is…

A: we have, fx,y=xy9x2+3y2 For limit to exist, if we take any curve y=fx through 0,0, the limit along…

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

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Q: Find the limit and discuss the continuity of the function. lim sin 1. (K. y)(27, 4) y lim 2. (x,…

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Q: Let zo = 0. Discuss if the limit of function f(2) = exists at zo- • If yes, then lim f(z) = z+z0 •…

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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: Show that the limit lim (r.y)(0,0) In(1 – a²) + yª r² + y does not exist.

A: First replace y=mx and then find the limit if the limit is dependent on m then the limit doesn't…

Q: Find the limit, if it exists, or explain that the limit doesn’t exist. (a) lim…

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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: 8. Find the limit, if it exists, or show that it does not exist: 2х-у a) lim (x,y)→(1,2) 4x²-y2…

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

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Q: Use the definition of the limit (e – 8) to show that 1 lim = i. z-i z

A: Limit Definition: Let f(z) be a function defined in some neighbourhood of z0. A complex number w0is…

Q: 4] [2M] Determine whether the limit exist in R for lim xsin(1/x²), (x# 0). x→0

A: Zero

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

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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: Show that the_limit exists : 2x²siny 2), lim (x,y)→(0,0) 2x² + y²

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Q: Let f(x,y,z)=x^2+4y^2+2z^2. Does the limit lim_(0,0,0)f(x,y,z) exist? If so, use generalized to 3…

A: Given:-             Let f(x,y,z)=x2+4y2+2z2. Does the limit lim_(0,0,0)f(x,y,z) exist? If so, use…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.