The joint function of X and Y is given by 0

Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

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Q: Determine if = f(x)=Vxis uniformly continous on the interval I [0, +)

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Q: Show that the function f(z)= Im(z) is nowhere differentiable.

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: Let f(x, y) = x* /I Evaluate f(3, 0)

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Q: Determine the two-variable function F(x, y) if Fy (x, y) = y sin(xy) + x given that x-² F(x₁ - ²) =…

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Q: f(x.y) = 7x?y",camate and af and ,campute

A: Given fx,y=7x2y4we have to find ∂f∂x =?    and   ∂f∂y=?

Q: The interval on which f(x) = 5 – 12x2 – 4x³ is concave up is: (-∞, –1) © (-1, 00) O (-0, 1) • (1,00)

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Q: f (æ, t) = e-t function fea - fu = 0 provides equality. True False

A: Given the function fx, t=ex-t We need to check the validity of fxx-ftt=0 to get the correct option.

Q: Differentiate the function. = In({ (4t+ 1)³ (4t-1)5 F'(t) = F(t) = In

A: The derivative of the function in the division form is given by the quotient rule which is given by-…

Q: Evaluate SIL. dydzdke, where E = {(x,y,z): (2+z12<x< 2, - (4 - z)2sy <(4 -2)12, 3<z 58}.

A: Given: The given integral is ∫∫∫Rdydzdx The given intervals are (y2+x2)12≤x≤2, -(4-z2)12≤y≤(4-z2)12,…

Q: When z = f(x,y), which of the following is true for the whole statement? O ddz = f"(x).dx² and dx2…

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Q: Finel the ralves of a anel b such that the function aV5-x tb-1 it Hax cos(TT Ix) 9 +1+ b(x²-7)…

A: Note: There is an error in question, for the given function a has 2 values but it cannot be possible…

Q: If a F (2) = xy+i (x² – y²), what is F (-1+2i)?

A: given  F(z)=xy+i(x2-y2) To find the value of  F(-1+2i)

Q: Let f(x, y) = (- (3z + y))°. Then

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Q: Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable…

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Q: Check that the equation x³ + y³ + z³ = x + y + z implicitly defines at least one differentiable…

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Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

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Q: Prove that dl = (Vu) x (Vv) - do.

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Q: OD Findof the following functions: 1) e" = In(x²y) – y² + 2x* 2) y t = (2x – 3)²

A: Find the derivative of the following function

Q: Find the domain of Hi function fr w =J 2x+3 -1

A: It is given that the function fx=2x+3-1. Find the domain of the function. It known that the root of…

Q: The function(x)= is concave down on which interval?

A: Given: f(x)=1x2+1

Q: Let z be a differentiable function of x and y related by the following equation: x + ² =(√y +…

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Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: Let X ~ Exp(λ). Find F(X) and E(X).

A: Let X ~ Exp(λ)The probability density function of X is fx(x)=e-λx   ;x&gt;0

Q: Find the interval(s) where f is concave up for f(x) -4x4-3x- 5x-10 0)

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Q: (b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.