[38] Evaluate f, 40yds where S is the portion of y=3x2+3z2 that lies behind y=6.

Q: Find: that: fl4) = -8 f'(4)= -8 %3D glx)=r

A: Given: g(x)=x f(x)f(4)=-8f'(4)=-8

Q: evaluate the Pirst and second deriugive of f) = 327+5csin 3x• %3D at x= 11 , 2.5 &3.7

A: To evaluate the first and second derivatives of f(x)

Q: Differentiate f(x) = (3x)n() for r > 0. %3D

A: To differentiate (variable)(variable) ,  we need to take logarithm both the side then to…

Q: Q3): If x fx + yfy = nf show that x²fxx + 2xyfxy + y² fyy = n(n – 1)f %3D

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Q: Q3/ Find f'(x) = y' %3D 1. y (2Vx-4)5 %3D 2. y = (x+2)2 %3D 3. f(x) = x2.- %3D x+3

A: Consider the given function. Q3 1. Consider the given function. y=2x-45 Find the derivative of the…

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

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Q: Find f. r0 - VD + Sx), 1) -9 X) =

A:

Q: dx 19. Evaluate using substitution f V5-4x-2x2

A: I have used method of substitutions

Q: f(x)= x2/5 Where it concave up/down?

A: To find the concavity of the given function.

Q: dy Suppose that 2r² – xy + y² = 1. Find dr

A:

Q: FInd the implicity differentiate x^2- 4xy + y^2= 4

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Q: Find & for f(r, y) = y- 4ry + 5y .3 2

A: Using partial derivative.

Q: Calculate y*)(0) for 0 < k < 5, where y = x* + ax³ + bx² + cx +d (with a, b, c, d the constants).

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Q: For Vx 3 evaluate y when y = 4. 2

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Q: write the domain in interval notation.

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Q: Find the general antiderivative of f(x) = 15x-3/5 and check the answer by differentiating. %3D

A: We have to integrate the function

Q: Calculate, f(t) from 5s² + 30 F(s) (s – 2)²(s² – 6s + 13) - |

A:

Q: Why is f'(x) approximated well by the difference quotient when Ax is very small?

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Q: What is the value of f(1) - 16B in J x³ Inx dx = f(x) ((1/4) Inx-B) + C?

A:

Q: f(x) = %3D 4 — т

A: We will approximate f(x) by the Taylor series. Taylor series of function fx at a is defined as:…

Q: D Determine where F(x) = ax' -3x -ax is concave up and concave down.

A:

Q: Find De f Re ー X - 2 2SXミ-1 y = P(x) = ーX+2

A: The domain of a function f(x) is the set of all values of x at which the function is defined i. e…

Q: e where r is jiven peu'ametor! Fnd f'6).

A:

Q: Not sure how to start problem

A: Given functions are We find g(f(x)) by replacing x by f(x) in g(x)

Q: 3x 8y Find f, and f, for f(x, y) = 2y 5x'

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Q: Find the general antiderivative of f (x) 25x-315 and check the answer by differentiating. %3D

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Q: Calculate L4 for f(x)=57cos⁡(x^2) over [2π/4,2π/2].

A: Given, f(x)=57cos(x2)   over [2π4,2π2] f(x)=57cos(x2)   over [π2,π]

Q: Given the function f(r) = 4r* + 36r + 567² %3D its f-intercept is its r-intercepts are

A: The x-intercept is the point where the graph of the function f(x) crosses the x-axis. To find…

Q: 6x + 6 If f(x) = find: %3D 4x + 4' f'(z) = f'(3) =

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Q: Which of the following is an antiderivative of f(x) = 12x³ - 9x2 + 8x – 3?

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Q: Find f(2) given that f(z) = 2r +5.

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Q: Q3: if f(x)= xy+2x-5y =2 then dy/dx3D a- b- C-

A: We know that dy/dx mean difernciate f(x) with x. From this we will get our answer.

Q: Q3 Find f-(x) for the following : 1- y = Jx-3 2- y = (2x³ + 1)'/5

A: For finding the inverse, we will replace x with y and y with x

Q: y" – 4y' = x2 By used Variation of Parameters Metho

A: Topic:- differential equations

Q: Calculate M6 for f(x) = √7x on [0,2]

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Q: 1. (D 2 + 3D + 2)y = 4t 2 By: (a) reduction of order, and (b) variation of parameters.

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Q: Vhich function is equivalent to y = 2(r + 3)+52 %3D Oy = 2r + 14 Oy = 2x + 12a + 23 Oy = 2x + 12r+…

A: y=2(x+3)2 +5

Q: Calculate R3 and L3 for f(x) = x² – 4x + 8 over [1,4]. %D (Give your answers as whole or exact…

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Q: What is the antiderivative of f'(r) = - 4x + 3

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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: Find fxxyzz for f(x, y, z) = z°y2in x. fxxyzz = -12z?y/x2 O fxxyzz = -12zylx fxxyzz = -12zylx2…

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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: 2x 10y Find f, and f, for f(x, y) = 5y 3x

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Q: Find the cdf of Z = 5(Y – 2). Write your final answer as a piecewise expression as was used in the…

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Q: Calculate h'(r) using the Product Rule if Mc)- (-3) (구+ ) = (2x – 3)(x² + 7) then h'(r) = ex' (x² +…

A: We will use product rule of derivative and comparing the terms with given terms of derivative to…

Q: Differentiate v1 +x² with respect to r.

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Q: Suppose that f(r, y) = x² – xy + y² – 4x + 4y with – 4 < x, y < 4. -

A: 1.)  Given Function is  f(x,y) =x2-xy+y2-4x+4y  with  -4≤x,y≤4  Then, fxx,y=2x-y-4…

Q: Consider f(x, y) = 57x2 +61ry+ 7y? f-(x, y) = %3D and fy(x, y) = %3D

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.