R(x) (x – 1) (x + 2)

Q: у" - 5y" 2y' + 24y = x + e-2x

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Q: - P(X 1) = - P(2 1) =

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Q: z2-ze coshw.K (z) z2– 2ze coshw.K+e2a -

A: The solution is given below. Hope this helps!

Q: a. f,(Xx)=x f2(x)=x² fa(x)=1-2x² b. f,(x)= e3x f2(x)=e5x fg(x)= e=* C. f,(x) = x-1 f2(x) = x'/2…

A: We have to choose the function that is linearly dependent on the given interval

Q: (c) x (x1, x2, x3) = 6x1x2x3 + +3+x}-I (d) ¤(x1, x2) = e-rl %3D 2x3+2x3+2x}+5 %3D X2+3

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Q: [x y 2 9 2 23 3 6 xy2] → Prove it.

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = (x2 + y2 + z2)-1/2

A: Differentiating with respect to x, keeping y and z as constants, we get

Q: 9. h(x) = 9x-3x'-12x – 10x-7 %3D a. h(x) → -∞ as x → -o and h(x) → -00 as b. h(x) → ∞ as x→ -00 and…

A: As h(x) is polynomial, it is always continuous . h(x)=9x4-3x3-12 x2-10x-7 h(x)=x4 (9-3x-…

Q: x = c e + c2t e“ O x"- 36x'+ 12x 0 6. O x"- 12x' + 36x = 0 %3D O x"+ 12x'- 36x = 0 O x" - 4x'+ 9x =…

A: for a differential equation having repeated roots m of auxillary equation thenthe solution or the…

Q: c) x + w²/x = t, x(0) = 0 and x(0) = 0

A: The given differential equation is, x''+ωn2x=t where x0=0 and x'0=0. It is required to find the…

Q: Choose the formula for finding the slope m of a nonverticalline that contains the two distinct…

A: Given two distinct points.

Q: (e) x+ 2x + 3x, = 0 (f) x- 3x +2r, 2x)- x +x = 0 X- 2r2 + 2rs -2x1 +x2 = 0 0. 2x) + 3x + 4x, = 0 (g)…

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Q: a) -x +y - z = 0 2y + z = 3 z = 0

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: i) (x-1)(x-2)(x-3). k) (x-1)³. j) (y-6) (y-4) (y + 1). 1) (x+2)³.

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Q: x2 - x + 2 = 0 over z3 [i

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Q: y show that = 0. . If z: x² + y² II

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Q: x-(1+iy) Q11: Express- in terms of z and z. (x-1)2+y2

A: Let z=x+iy and z bar =x-iy

Q: 3) Given that f(x) = 2x+ 5 g(x) = 2x – 6 and h(x) = x- 5 i) f(-4) = iv) h,f(x) i1) h[f(-6)] = v)…

A: Explained below

Q: Q2:- (x²-9 | X # -3 A) f(x) x+3 %3D -6 x = -3 Is f cont. at x =-3 ?

A: Continuity of function

Q: 3 x = y + z- w = 2 -x + 2y - z - w = -1 2x - y - z+ w = 4 x + 3y - 2z - 3w = 6

A: 3

Q: b. Min z = 4x1+ 2x2 s.t. 3x1 + x2 2 27 -X1 - X2 <21 X1 + 2x2 2 30 X1 and x2 are unrestricted .

A: Given: Minz=4x1+2x2s.t.3x1+x2≥27−x1−x2≤21x1+2x2≥30

Q: f(z) = 2(x – 5)² + 3. - f (x) is invertible for which values of x?

A: Given function is: fx=2x-52+3 Then we get,…

Q: 5x + 2 8. Let z(r) = Algebraically determine z-(1). 4r -3

A: Solution of the problem as follows

Q: r²[(x²-y²)²] 1²₂5²² du dt x+y

A:

Q: 0,x1 x+2,x<-1 f (x)= %3D 2,x2-1

A: Interval notation is a way to describe continuous sets of real numbers by the numbers that bound…

Q: 1 of f(z): is z2+2z+2 %3D

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Q: f (x) = 2(x - 5)2+ 3. f (x) is invertible for which values of x?

A: Given that,

Q: 0, x4. then P(2<X <4) is equal to

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (2) F(x)= | V1+sect dt [ Hint : | V1+sect dt =- V1+ sect dt ]

A: Given: Fx=∫xπ1+sectdt according to fundamental theorem of calculus derivative of…

Q: a) z=-x² + y² c) z² = x² + 2y² e) x² + y²-z² = 1 b) z=-x²-2y² d) -x² - y² + z² = 1

A: match the following quadratic surfaces with the following equations (a) z=-x2+y2

Q: x² 2. =25 ty-3)"=25-x² 3= J25-X 3525-x %3D Simpliy+ this s , like Idid herel

A:

Q: What is r' (x) when r(x) = In (x + 2x2 + 3x + 1)? %3D Select the correct answer below: O In (3x2 +…

A: Given: r(x)=lnx3+2x2+3x+1 We have to find the r'(x)

Q: 3. f(x) = (3x – 2)* %3D 4. f(x) = (x² + 1)° (xr? – 1)² | (2x – 6)* f(x) = (x + 7)7 5. -2 6. f(x) =…

A: See the details solution in below

Q: Q2:- (x²-9 A) f(x) = |X # -3 x+3 -6 x = -3 Is f cont. at x =-3 ?

A: We can concept of limit in order to solve the given problem.

Q: 2 3. y' + ²y = -x²y²cos x

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Q: f(x, y) = x²y + 4y and x = st, y = 2t - 3s. Use Chain Rule to find of and of (Write your answers in…

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Q: X₁ + X₂ Q2: Let X₁-G(4,3) and X₂G(2,3) by mgf find dist. of Y=X₁ +X₂. ===

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Q: r(x) = (/2x + 1 - x²)-1 r'(x) =

A: Given query is to find the derivative of the expression.

Q: (1+x}(1-2x) 1+4x (a (-x)(1-x) (p

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Q: 3) all x² -2x-3 a) g(x) %3D x-4x +3 x-3 b) f(x) = %3D x -9 8x-16 c) h(x) = %3D x* -8x +16x

A: a) g(x)= x2-2x-3x2-4x+3              = x+1x-3x-1x-3    g(x) =x+1x-1…

Q: 4 %3D X2+2x-15 is X-3 S+X

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Q: -. g(x) = Vx + 7 i. Domain: (-7,00) Preview x + 30 . h(x) : 4 - i. Domain: (-30,4)U(4,00) Preview

A: Given query is to find the domain for the function.

Q: 2x4 - 3x2 - 12x + 6 at 0 and -2 to deter f(x) = ero exists between the two values.

A: we have to evaluate the f(x)=2x4-3x2-12x+6 at x=0 and x=-2and to determine if the intermidiate value…

Q: x +x-6 F(x)%3D at x= - x+3

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Q: Solve for (f o g)(x) , when x = -1 f(x) = 5x + 1 g(x) = 3x - 4 Solve for (g o f)(x) , when x = -1…

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Q: I need help checking my answers. Thank you for your help.

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Q: Your major online bookstore is in direct competition with Amazon.com, BN.com, and BooksAMillion.com.…

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Q: 2. Given f(x) = 3x + 2 and g(x) = x - 2x +3. Evaluate 2g(f(-4)) in simplest form. %3D %3D

A: "Since you have asked multiple question, as per our guidelines we will solve the first question for…

Q: The characteristic equation of the ODE y (3) -2y'+y²=0 is defined by p3 – 2=0 3 – 2r+1=0 r³-2r=0…

A: We have to find the characteristic equation of the ODE as given y3-2y'+y2=0

Q: 2xvx2 + 1 Find g(a – 1) if (g ojof•h)(x) where f (x) = x + 1 , %3D x² + 1 h(x) =, and j(x) = Vx .

A:

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.