a²f x²-y² дудх x2+y2

Q: What is the derivative of y= 3Arcsin xº, 3 Arcsin x In 3 A y' = 1 - xa 3 Arcsin x* In 3 3 B y' : (а…

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Q: Find the derivative of the function f (x, y) = x²y + y²z: at Po(1,2,3) in the direction of û = 2î –…

A: To find the derivative of the function f(x,y)=x2y+y2z at P0(1,2,3) in the direction of…

Q: If (x, y) moves from (x0, y0) to a point (x0 + dx, y0 + dy) nearby, how can you estimate the…

A: The resulting change in function f (x, y) is given as:

Q: Find the equation of the line tangent to the graph of f(x) = – = -3 cos (x) at x = 3 m(x – xo). You…

A: given: the function f(x)=-3cos(x) the point is x=-π3

Q: Solve using Substitution Method. y(x Tan x + In y)dx + Tan x dy 0

A: The substitution method as follows, y (x tanx + ln y) dx + tanx dy = 0

Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

A:

Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: Find the derivative of the follourng funchion y=x sin'x %3D

A: We have to find the derivative of the given function   The given function is y=x sin-1x3it can…

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: Find the derivative of f (z) = (2° – 5z) (2² + 6z – 6). a va la sin (a) f' (포) 3DD Please explain,…

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Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

Q: What is the derivative of cosh-1(xy) + elog x = sec3(y2)

A:

Q: Find the most general antiderivative of f(x) = -3e" + 10 sec2 (x), where - < x < 2 Note: Any…

A: According to the given information it is required to calculate the antiderivative of the function:

Q: 3x V1-x x = 0. y(x) = at Equation of the tangent line

A: Given,           yx=3x1-x2 at x=0

Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

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Q: fro(x- dt show that = f(x). dx y 3

A: y=12∫0xft x-t2 dt

Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

A:

Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: Find the maximum rate of change of f at the given point and the direction in which it occur f(x, y)…

A: Topic- Vectro

Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: What is the derivative of h(x, y) = e"Y at (2, 3) in the direction at an angle of 7 from the…

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Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1x2+1

Q: Find an equation of the line tangent to graph of y =x2 + sin (Ex) at x=-1. A. 2x - y+2 = 0 B. 2x +…

A: To find the equation of tangent line of the given graph.

Q: Find the relative extrema (if any) of the function f(x) = sin 2x ; over the interval (0, π).

A:

Q: dy Exc:" of y = tanh (x5 – 5x)² --

A: Solution:Given         y=tanh4(x5-5x)2  To find dydxFormula:ddx(xn)=nxn-1ddx(tanh x)=sech2x

Q: 3. f sin³y(2-3cosy)² dy

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Q: 23-4z2-2一4 y = %3D 1+ Va

A:

Q: Let sin(r-y) ||| + \y| +0 (x, y) = (0, 0) f(x, y) Is f continues at the origin? Why?

A: Solved below

Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

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Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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Q: Find f'(x)'f f (x)= arctan (Inx) %3D

A: Using composite function formula.

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

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Q: f(x csc² 2x - x cos 2x)dx

A: The given integral is ∫xcsc22x-xcos2xdx. The objective is to solve the given integral. Following…

Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

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Q: Test for homogeneity

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Q: Find the derivative of the function f(z) = 3z² +7z at I = a.

A: Given,            f(x) =3x2 + 7x  and x=a

Q: -2 In(x) Consider the function f(x, y) = 3y

A: We have to find the derivative of the function f(x,y) in the direction u=-5,2.…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: Let f(x,y) = x^2 y + e^xy sin y.   At Point (1,0) State the direction where the function…

A: Given: fx,y=x2y+exysiny