Find the domain of h(x) = V36 – 2x.

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: To find the critical points we solve dy/dx=0

Q: f(x) = (13 + 6t² + 1) dt

A: SOLUTION-

Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: Find the area of a triangle bounded by the y-axis, the line f(x)=10−2x, and the line perpendicular…

A: y=10-2x here coefficient of x is -2 so the slope of the line is m=-2 and the perpendicular line…

Q: f(x) = 2+ 3x² – 8x3 -

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Q: Find the linearization of the function f(x) = x^8 at x = 1

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Q: Find the length y=(x+2)^3/2 for x in the range 0≤x≤2.

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Q: 12x the axis, x n bounded by the curves = x2 +4

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Q: The function f(x, y) = -3y + 2√√ry is a

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Q: Find d2y/dx2 implicitly in terms of x and y.    x2y − 4x = 5

A: To find the second derivative of y implicitly in terms of x and y.

Q: Solve the DE f'(x) = 5x given that f(0) = 3. %3D A y +3

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Q: write the domain in interval notation.

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Q: Find the domain of the function f(x,y)= exy/ x-y2

A: Answer-

Q: Find the linearisation of f(x) = 4√x at a = 16. Use this to estimate 4√ 15

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Q: Find the value of x and y which satisfy 2x + 3y = 8 and whose product is a minimum.

A: To solve the following problem

Q: Differentiate the function. y = (3x- 2)² (1 –x³)² dy

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Q: Find the area of a triangle bounded by the y axis, the line f(x)=4−(6/7x) and the line…

A: Formula Used: Area of triangle is :                                   Where,  b is base of triangle…

Q: 6. Find the domain of y = Vx+ 4x + 5x + 2 + Jxl-|x+1]

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Q: find the Domair y=3+ +Vx X-3

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Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: 14. The f'(4) for y = v3x2 + 1

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Q: Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

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Q: Find the linearization for f(r) 10, and use it to approximate 12 near a=

A: We want to find the approximate value of 112 by linear approximation of the function ,fx=1x by…

Q: Find the relative maximum and minimum values. f(xy) = e 6x2 + 4y2 + 8

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Q: find all possible functions with the givenderivative. y' = 2x - 1

A: Given y'=2x-1 that is  dydx=2x-1 Integrating with respect to x, ⇒y=x2-x+C Where C is the constant of…

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

A:

Q: Find the linearization of the function at x = 1.* f (x) 2x - 3x + 7 %3D

A: From the given problem:   fx=2x3-3x+7 ; x=1   As we know that the expression for linear…

Q: I Sdve for dy using the four-step rule 2. y = x"- x 5X-3 ソ= 4- 3X

A: We have to solve the problem

Q: Let_y=x² +5x³-4x+1 then dy- ||

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Q: Find the area of a triangle bounded by the y axis, the line f(x)=8−13x, and the line perpendicular…

A: Recall : Area of the triangle with three points x1,y1,x2,y2 and x3,y3 :            A=…

Q: Find d3y of the function y=xln1/x.

A: Given: Calculation:

Q: The region in the first quadrant bounded by the x-axis and f (x) = 3x – x² is

A: The graph of region bounded by curves y=3x-x^2 and x-axis is

Q: Y = 0.75X + 0.0042X2 – 0.00023x3 At what level of X, the output will be maximum?

A: Given: .

Q: Find the maximum value of 5x2 - 4xy+ 8y subject to x+y? = 1..

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Q: Evaluate [ T 1-x² x² + y² dydx.

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Q: Find the linearization of f(x) = V16 – x² at a = 3. %3D

A: Given: The formula used for linearization:

Q: What is the DE for A(x^2)+Bx+C using elimination of arbitrary constants.

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Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

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Q: Find the extrema of f(x,y) = -2x² + y taken on the graph of x + y? = 0.

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Q: y = v1 - x2 from a = 0 to r = ;

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Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

Q: of the function. + 3y + 11

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Q: find the critical point and classify the function f(x,y) =xlny +x2 -4x-5y+8

A: Answer

Q: dz Find from the equation x*y+ x z+ z² = 4 ax

A: We differentiate both sides with respect to x, considering z is a function of x.

Q: f(x) = v2x2 – 13 s %3D -

A:

Q: Consider the function y= g(I)= -z² + 3c + 6,

A: The derivative of the function f(x) with respect to x is given as .

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: Find DF of fcx,y)=x²e° at the point (-2,0)-

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Q: Q2 Find2 of y = 4x/x+ vã at x=1? %3D

A: