Find and classify the points of discontinuity. х2 — 4 f(x) : х2 — х — 6

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: Identify the removable discontinuity. x2 – 16 f(x) : X – 4 (x, y) =

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Q: G) for G) For anycurve, x= 3t,y=312,2=2t3, Show that 6 -

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Q: In(x – y) 9 – x² – y² · /x² + y? – 4 d and sketch the domain of f(x, y)

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Q: Find the convolution between x(t) = 2 rect and h(t) =rect() %3D

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Q: -3r 10 f(x) : r2--20 C, r= 5 What value of C would make f(x) continuous at r 5?

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Q: f(x,y) = x2y+1 find and sketch the domain

A: The given function is: f(x,y) = x2y+1 And, its graph is:

Q: Use the convolution theorem to find f (t) 14 l(s+2)(s-5))

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Q: Find the convolution f (t ) *g(t) f(t)=t^2,g(t)=cost

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Q: (a) (Xn+r)nzo for fixed r≥ 0,

A: Markov chain: A Markov process with discrete time and discrete state space is known as Markov chain.…

Q: Find the local extreme values of ƒ(x, y) = x2y on the line x + y = 3.

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Q: The function is x z = y² What is 8²% dy² 2/21/23

A: Let's find second partial derivative of given function.

Q: For T: R5→R3 and nullity(T) = 2, find rank(T).

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Q: Hiw Find dy for the followng functions- 1-5x +X 2+x 3. y= lacsinfe}} %3D

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Q: Find fry for the function f(x, y) = x²? – xy? – 7y +3. %3D

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Q: Consider y = xe^x on the interval [-5, 0]

A: In order to find global minima of the function, check the values of the function at end points and…

Q: Q Find the domain of y 1- Vx + V+ 3x-x – 3

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Q: Find y" from x =t +7, y = 6t -1

A: Answer and explanation is given below

Q: Let f(x, y) = 160 2x2-3y² 2a? – For which value(s) of y is f(4, y) = 10? y =

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Q: For the function f(x,y) = 8x² + 7y², find f(x + h,y)-f(x,y) = h f(x + h,y)-f(x,y) h

A: Given, f(x,y)=8x2+7y2

Q: Q2) Find Fxx, Fyy and Fyx For the function F(x,y) = (x+y) (y + 1)* .

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Q: Q10: Determine the set of point where f(z) = 6z2 – 27 – 4i|z|2 is analytic. -

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Q: Q2. Find of y = 4x/x + v at x=1? dr

A: We have to find the dydx of y=4xx+x at x=1.

Q: What is the domain of h(x, y) = Vx - y?

A: Given: hx,y=x-y we know that for domain of square root function inside of root not has to be greater…

Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

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Q: J 5(x) =-J5(x) ylgn O İhi O

A: We have to solve given problem:

Q: hup lict funcrion F(xig) = x?y -eto =0 P(e, 1) Find y" (e) = ?

A: Here to use implicit diffrentiation method for solving the problem

Q: Find (i) fx (x) (ii) fy V) (iii) are X & Y indepdent? (iv) f, (x/y) (v) (y/x).

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Q: Q4: Find and classify the extreme points of f (x, y) = 3x?y+y3 - 3x2 – 3y2 +2.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: g(x) is concave down at (-7,-3), concave up at (7, 10), and has an inflection point at (2, 4).

A: Given :- function is concave down at (-7,-3) concave up at(7,10) and inflection point is (2,4)…

Q: Find dz implicitly of the relation r + y³ = 3ry.

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Q: Find fyx, y) for the function flx,y)=x*-7x3y2+6xy³ + 4y4 O-28y O -15y2 O 76x2 O 24x

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Q: OLetL)%3DXD 3X-/0 when x+2-Fénd a value ff(2)that wall !! X-2 make fis Continueus at X-2

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Q: Find the DE by eliminating the arbitrary constants |.cʻy² = xCx- )° %3D

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Q: Q5 A) find dr for the function y = x' + Inx

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

Q: 6x +5y find ху - 8 dh and For the function h(x,y)= dy dy

A: It is differentiation problem.

Q: 3 S(x) = 6x² + x – 7 Find the coordinates of the point of inflection on and prove that it is a point…

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Q: Q3: Find the aven between the curve y,= x+2 and the Carve Y2=-2X+5

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

Q: Q3) a) find f sec³ x dx

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Q: For the function f(x,y) = 5x² + 6y², find f(x + h,y)-f(x,y) h 11 f(x + h,y)-f(x,y) h

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Q: Find the local extreme values of ƒ(x, y) = x2 + y2 - 4y + 9.

A: Given: fx,y=x2+y2-4y+9

Q: Q17 It z = f(x, y) and z* - x² = x²y°z? * and dz Find:

A: We will use basic differential calculus to solve the three parts of this question.

Q: Q4. Calculate div F where F = grad(x' + y³ + z³ - 3xyz).

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Q: Q2/ Evaluate f S (x² -2yx)dxdy using two point in x - axis and three point in y- axis.

A: The solution is given below

Q: Suppose that f(x, y) = 32 y at which {(x, y) | æ² + y² < 3²}.

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Q: Differentiate with respect to t 100 = x2 + y2

A: give equation ;- 100=X2+Y2 when we differentiate above equation with respect to t , we get

Q: nimize Z = (-1)*(X, abjected to, X, + X2 + X3 s 7 + X. - Xo <-

A: Introduction: The Simplex method is a method for solving linear programming models by hand by…

Q: Hiw.r provethat D2f +32f= y=o far the functionel xe -2y Coos 2X %3D

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Q: Compute Δy/ Δx for the interval [2,4] where y = 5x−7.

A: ∆y∆x for function y=f(x) for the interval [a,b] = f(b)-f(a)b-a

Q: Q3) Find fog(x), gof(x), D, D fog' gof x+2e f(x) = » g(x) = vx – 2 %3D 2

A: Solution:-

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.