A) Find for the following functions: 5x+1 1- y = 2 va 2- y = v2t + 2t t = x2 - 3

Q: Find y=f(x), if f''(x)=3x^2, f'(0)=-7 and f(0)=2.

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Q: Plot the following functions 1. y = - v2x +1 2. у %3D (х — 1)3+2 3. y =- 2x

A: 1. Plot of y=-2x+1 is shown in below figure:

Q: If x = f(/y+ 1) then, 2Vy f (Vy+1) 1. y' =

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Q: Differentiate the given functions 1)y=-2 2)y=x^7/3 3)y=x^3.7 4)y=pir^2

A: Derivative the function

Q: find the specific function values. ƒ(x, y) = x2 + xy6 ƒ(-3, -2)

A: Given function:

Q: Find f"(1)given f(x) = x Vx + 5x Зх. 2.

A: Given function is : fx=x2 x+5x2-3x=x2 x12+5x2-3x=x52+5x2-3x To find the value of f''1

Q: Find two nontrivial functions f(x) and g(x) so f(g(x))=(1−3x)^2

A: f(x)= x²

Q: If f(x) = 3 find f'(1). %3D 22

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Q: Differentiate the function below. y= (x2 + 4) (x² – 2) 8 d [(x? +4) (x² - 2) ® _ = O %3D dx

A: Ans is given below

Q: find the specific function values. ƒ(x, y) = x2 + xy5 ƒ(2, 3)

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Q: Consider a function of 2 variable f(x, y) = 2x³y² – 5x²y* + 3x³ – 4y³ af and Əx af Find ду

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Q: HW 1-Find the domain for each function : (1) f(x,y)=Vy-x-2 (2) f(x,y)= In(x²+y² -4)

A: We have to find the domain from the given functions

Q: Q3// Draw the function 1 y = 2 sec-1. Зх + 1

A: Our objective is to draw the graph of the function.

Q: Differentiate the given function, 1. y = vx – 3(x² – 1) 2. y = (2-x)(1+x) Vx+1

A: 1. Given function is y=x-3x2-1. To differentiate the given function. Solution: Product rule of…

Q: Given f(x, y) = 5æy® - 8x°y. Compute: ||

A: Given  f(x,y) = 5xy6 - 8x5y

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

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Q: Find domain and range F(x,y)= Vx-1

A: Since you have asked multiple questions in a single request, as per policy, only the first question…

Q: Plot the following functions 1. y = -V2x +1 2. y = (x- 1)3 + 2

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Q: Find the indicated value of the function f(x,y) = 2x + 6y - 2. f(4, – 2)

A: We the the value of f(4,-2).We Put the given points in the given function.

Q: II. Differentiate the given functions: 1. у %3D 3x2 — 2х 2. y = (x + 2)(x² – 4) 1 3.y = 2tvt +

A: To differentiate the given functions : 1) y = 3x2 - 2x 2) y = (x + 2)(x2 - 4) 3) y = 2tt + 1t…

Q: Find the indicated value of the function f(x,y,z)=2x-7y + 4z³ -7. f(6, -5,3) f(6, -5,3)=

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Q: Ex(20):- Locate all relative maxima and minima of f (x, y) = (x – 2)² + (y+1)² ¬

A: Find the all relative maxima and minima of f(x,y)=(x-2)2+(y+1)2 now find  fx=2(x-2) and fy=2(y+1)…

Q: If f(x) = (13 + 6t2 + 3)dt then f''(x) =

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Q: Find a function y(x) such that 4yy' = x and y(4) = 6

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Q: Find the function satisfying y' x + 3 and y(0) = 2 ... 2y + 5

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Q: (a) If h(x) = f(g(x)), find h'(1). (b) If H(x) = g(f(x)), find H'(1). %3D

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Q: If F(x)=[ -dt , find F' (3). 2t 2

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Q: Determine if (x² – 4, if x < 3 g(x) = %3D (Vx – 2, if 3 < x is differentiable at x = 3.

A: Let f be a real function. Let a be any point in its domain. If limx→afx  exist and equal to fa, Then…

Q: If f(y) = V4 - 7y, find f'(y). Use exact values.

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Q: If f(x) = [(1³ + 6r² + 1) dt

A: Here, the given function is: f(x)=∫0xt3+6t2+1dt...(1) Note that, the Fundamental Theorem of Calculus…

Q: Evaluate the function: S 4ry(6+y/2)dy

A: topic - indefinite integral

Q: State the range of f (x) 1 3x+4 = 4 {y e R]y± - } O {y e R|y>0 } 4 {y e R|y> O {y e R|y#0 }

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Q: Differentiate the function. y = V x2 + 2x

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Q: Find the maximum and minimum values of the function f(x,y)=2x^2+3y^2−4x−5 on the domain x^2+y^2≤9.

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Q: Plot the following functions 1. y = - V2x +1 2х + 1 2. y = (x – 1)3 + 2 3. y =-1 3. У 2x

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Plot the following functions 1. y = - V2x +1 2. y = (x - 1)3 + 2 3. y =-1 2x

A: As per our guideline we are allowed to do 1 question or 3 subparts at a time. Please post other…

Q: Q2// Find the domain and range of the following functions: 1 1) y 2) y = Vx +4x +3 1 1 * +2

A: Given: 1) y=11-1x+22) y=x2+4x+3

Q: Differentiate the function. (3y + 1)4' Vy2 + 1 ) G(y) = In G'(y)

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Q: Plot the following functions 1. y = - V2x + 1 2. y = (x- 1) + 2 3. y=-1 2x 4. y? = 6 -x 5. y = 1-…

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Q: Q1) Find fyxx of the function:

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Q: Find a function y(x) such that 4yy' = x and y(4) = 7.

A: Answer

Q: Find the values of c and d that make the function 6x if x 2 continuous. с — d =

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Q: Find the slope of the function f(x) = V5x at x = 5. V5/2 -25/2 1/2

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Q: В. Find az if z = f(x, y) is implicitly defined as a function of x and y for the equation below…

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Q: find the specific function values ƒ(x, y) = x2 + xy3 a. ƒ(0, 0) b. ƒ(2, 3)

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Q: Find range of function f(x): b) f(x)= (2 – x)V 4x – x²,xE (0, 4) -

A: b)   f(x)=(2-x)4x-x2 , x∈(0,4)         plot the function on the graph

Q: Draw the function 1 y = 2 sec-1 3x + 1

A: Given , y=2sec-113x+1

Q: 2 Ax, y) = V 16 – x – 4y²

A: Given function  fx,y=16-x2-4y2fx,y=16-x2+4y2 Domain pf the function  16-x2+4y2≥0x2+4y2≤16x216+y24≤1…

Q: Find and for the functions: ax ду 1 f(x, y) = x Jy + y5 – :

A:

Q: Find y' if 3x2- (ry?) = 2y.

A: Given that, 3x2-xy212=2y3 Find the derivative of the given equation.