Let / (r) – = 2x 3z+2 and g (r) 6x 5x+2. What is the rule for (g-f) (x)? o (g-) ()- 4 2x o (g-) (2) --2a +3 +5x o (g-f) (r) =-2r +9z o (g-) (z) - 2x 92 + 5x 2.r 5x

Q: if y3-3ax2+x3=0,then prove that y2+ 2a2x2y-5=0

A: Let dy/dx= y1 and d2/dx2=y2 And We will use the product rule of differentiation.

Q: 7 --y2 Then 2 5 Q2: If z = –x² az + 5x ду az 7y ||

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Q: if y3-3ax2+x3=0 ,then prove that y2+2a2x2y-5=0

A:

Q: 8) Is (x+3) a factor of x4 + 2x2 + 17x – 48 Drop coefficients onto top line

A: Given,  x4+2x2+17x-48

Q: If y= (5x+1) (2x-1-1n7), then y’ will be (5X+1) 2/X2 +1/7

A: Given that  If y= (5x+1) (2x-1-1n7), then y’ will be (5X+1) 2/X2 +1/7

Q: Maximize B=6xy^2​, where x and y are positive numbers such that x+y^2=4.

A:

Q: - 2 2 x² +1 x+2 x-3 x2 2 (Be sure to find the restrictions!) - x- 6

A: Restriction : x must not be equal to -2 and 3 Solution : x= -3

Q: Q1. Find the general solution for the non-homogen 1st OLDE using undetermined coefficient method.…

A: Given Y'=-3-456Y+5-6ex

Q: 2 If f(x) = x+ 8x + 12 and g(x) = x + 6x + 8 then (2) (Make sure your answer is fully simplified %3D…

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Q: 8²z 8. If z = x + y Inxy, show that x- 8 z + x² 8²z 8y² 8x8y

A:

Q: 3. Divide x+4x-3x-2 by X-2) then divide if CX-2) isa factor of x² t4x-3y-2 why?

A: We have to divide (x3 + 4x2 - 3x - 2) by (x - 2)  Then ,

Q: tion 20 +4)/2 = > aj,æ“ for || then 16a3 2 k-0

A: We have to find the value of the given condition

Q: Find the total ancd neguon between x-axis and the gruph of y==X2 - 3X, -7sx52

A:

Q: 82z 8. If z = x + y lnxy, show that x- 82z + ミy2 82z 8y2 8x2 δχδν

A:

Q: 82z 82z + 8x2 82z If z = x + y lnxy, show that x- = y², y2. 8y2 ID 8x8y

A: Given, z=x+ylnxy We need to show that,    xδ2zδx2+δ2zδxδy=y2δ2zδy2

Q: What is the coefficient of (x^8)(y^12) in the expansion of (2x+3y)^20

A:

Q: What happens to y=fx) when you replace y with -4y? O vertical stretch by a factor of 4 and a…

A: Vertical stretch: The graph of y=dfx is the vertical stretch of the graph of y=fx by a factor d,…

Q: if x 0 -

A:

Q: 2. If 4x² – 9y² = 27, show that y" 9y5

A:

Q: 2. If x =-1 and z = 2y = -3x, find the value of 3xy-z 1+3x²z

A:

Q: What is the correct evaluation of x2 - y2 - z2, when x is equal to -2, y is equal to 3 and z is…

A:

Q: 1. Differentiate: y = 3(x²-1) A. (In 3) 3(x²-1) B. (2x) 3(x²-1) C. 2x (In 3) (3**-1) D. x²(In…

A:

Q: 2s Use Convolution to find L-1[- (s²+4)2-

A: Given: L-12ss2+42

Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: If y3-3ax2+x3=0,then prove that y2+2a2x2y-5=0

A: Solution of this question is

Q: - -X-4-z=4 2X- 2X+G-3z=- X 0-42=3

A:

Q: What is the correct evaluation of 3x - 2y, when x is equal to -1 and y is equal to 1?

A: We have to find the correct evaluation of 3x - 2y, when x is equal to -1 and y is equal to 1.

Q: 4. In x2 -4x + 4 - b2 = 0, find the value of x. %3D

A: Topic:- algebra

Q: -If x(z) = 2z + 5z-1 + 6z-3 – z4 find x(n). %3D

A: The given signal is,xz=2z+5z-1+6z-3-z4

Q: 6, Find the domain of y = 4V4x+2. O x2 -2 x2- 1/2 1/2

A:

Q: Consider 2a – 3y² = 8

A: Differentiate wrt x

Q: f(x) -10 -8 -6 –4 -2 4 8 10 1 -2 -3 -4 - 6 -가 -8F 2. 1.

A:

Q: 1) x² + 9y² + 9z² = 81 2) 9x2 + y² + 9z² = 81 3) 9æ? + 9y? + z² = 81

A: Given equations 1)x^2+9y^2+9z^2=81 2)9x^2+y^2+9z^2=81 3)9x^2+9y^2+z^2=81

Q: If z1 = -4 + j5, z2 = -3 - j2, and z3 = 2 - j3 , what is the simplified form of z – z + 2 ? %3D

A:

Q: (2) Determine k such kx² – 4x +- = 0 that has real and different solutions.

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Find the 3rd term of (x + 2)³.

A:

Q: Show that |Aut(Z2 × Z2)| = 6

A:

Q: 5lim V3+x-J3 8→0

A:

Q: Salx) = 212-4.87x+ 3,2x² -0,53x3 S(K) =FSzcx) = -30,2 +27 53 x- , 6x+ 0,69X, S(x) = 2イ- 40,争K+…

A:

Q: 9. For Ax) = -4x+2, find (x) when x==1. %3D а. С. 2 b. -2 d. 6

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Q: -5 -3 -1 -2 -3 -4 -5+ f(z) = %3D (b) 5- -10 -6 -7 -6 -3

A:

Q: f (2) 2. Find if Ar) -(1-x²)(* -1) =

A:

Q: What is the coefficient of x'y' when (x – 2y)² is expanded using the - Binomial Theorem?

A:

Q: et xー4x-i7x +12 . Find xS. y'= 3x=-8K-17 y"- 6K -マ y"! =6' i2 y= x- =人 - 6x2 + 3x-2,what is 12

A:

Q: (2) Determinek such kx - 4x+- =0 that has real and different solutions.

A:

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.5x2 −…

A:

Q: If (x1 , y1) = (-3, 1) and (x2 , y2) = (-2, 4), find (y2 - y1) / (x2 - x1)

A: Given, x1, y1=-3, 1x2, y2=-2, 4

Q: - 7x+ 3y+4z = -6 -23x+23y+kz =-31 -4x+ 5y+7z= -6 we must have, k +

A: We have to find the conditional value of k such that the following system is consistent.…

Q: Use generating functions to determine the number of integer solutions for x + y + 2z = 29, x2-2, y >…

A: Given that x+y+2z=29 As for each x,y,z are non negative. The variable for x is, The variable for y…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.