1. Expand x³y²(x + y)12. E15.(15) xn+3y15-n ,15-п а. n 12 b. Eo () xn+3y14–n ELo (5) xn+3y14-n С. Zn=0 n d. 4-n п Σ 12 Ln=0 (5) x"y14+n е.

Q: If y (4x + 6)*, find y'(1). O 10ln(10) + 4 %3D O In(10) + 2/5 O 10ln(10) - 2/5 O In(10) - /5 O…

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Q: Given the following linear system of ODE: V₁' = 4y1+2V2 V₂' = 10/1-4/2 what is the type of the…

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Q: dealing with one piece at à tir Deal with the "T+" first. 10. cos (* - a) = cos (T + (를 -a)) = 11.…

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

Q: 3. L {e-5t + t²}

A: We have to solve the given laplace transform.

Q: Express the following in the form In(x + a) + ln(x − a) + ln(x² + b), with a, b = N: In(x¹ − 1) = |…

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Q: Let h(t) = (0 sin(t) Find L {h(t)}. S 0π/2 e-лs/2

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Q: 21 – 17x + 35 x- 5 3 lim .. A. D. 9 В. 5 С. 7 Е. 11

A: We can make it easier for you.

Q: A. y = x² + 2 Е. у 3 (х- 2)2 I. y= 2x² B. y = -x² + 2 F. y = - (x + 2)² J. y = -2x² C. y = |x| + 2…

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

Q: x²+ 4x – 21 - . ... lim х- 3 А. 6 В. С. 10 D. 12 8 Е. 14

A: solution of the given problem is below    ...

Q: 5.PT. PLN has $140000 to invest. The alternative investments and the corresponding annual returns…

A: According tot he given information it is required to form an linear programming problem for the…

Q: 1 3. JxIn(2x+1)dx 3 а. 8. 1 - In (3) 8. (e)u d. (In(3) - 1) с. - In 4 е. in

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Q: Solve the ODE xdy/dx + y = 0 when x = 4 and y = 6 а. у %3D 1/х + 23/4 b. None of the choices С. ху…

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Q: 5.Jf(x) =- 3x + 7 g(x) = 2x - 8 Find f(g(x))

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Q: 6x +1 12. j ** dx = x +9 A. 6ln(x² +9)+ 3arctan +C 3 B. 3ln(x +9)+ arctan +C 3 1 C. 3ln(x²…

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Q: Sxª+a*+ a®) dx = %3D O a. xa+1 ax +C Ina а. a + 1 O b. xª+1 a + 1 ax +aªx +c Ina O c. xa+1 +а\ina +…

A: Consider the given integral. ∫xa+ax+aadx Rewrite the given integral as separate integrals.…

Q: Consider the parametric curve: x = ln (8t) y = 5t³ Which integral gives the arc length of the curve…

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Q: 24. 2n n=1 а. 1 b. 0 с. -1 d. 2 e. Divergent

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Q: If y1=x2+x°is a solution for x²y"-4xy'+6y=0, then the second solution is Select one: a. -In(x+1) O…

A: we have to solve given problem:

Q: Evaluate L{e * (sin 3t – cosh 5t)} . 3 s+5 A. (s+5) +9 (s+5) +25 3. S-5 В. (s-5)-9 (s-5) +25 C. S+5…

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Q: 4. √ (3x² + 4x − 5). 8(r³+2x²–5x+5) dx

A: We have to find solutions

Q: Г. 5 1, г)ах — 9, g(x)dx 8 Compute: -[о g(x)dx b.) == 5 3f(х)dx %— с.) .5 f(x)dx d.) 2 "/Г 5…

A: Given,

Q: Solve the following ODE y +2Y +y=x + ex (C1 + x C2) e* + (x-2) + e²x / 9 .a O (C1 + x C2) e* -2 +…

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Q: 4 – x lim x→4 5 – Vx² + 9 А. 2 D. 4 5 3 В. 10 Е. C. 10 С. 7.

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Q: 2/3 /13 Find )

A: Given  x23x2+33x2+2x-16 Derivative is calculated as shown below

Q: (iv) 15-22 dr. u = (v) S 15 · T/9 – x² dx. 9-z (vi) J +15 da. u=

A: iv) 15x2/sqrt(9-x2) v) 15 pi sqrt(9-x2) vi) 9x/(x2+15).

Q: (Зх — 1) (x² – 1) A B (x + 1) (x – 1) A = %3D В (Зх — 1) dx (x² – 1) - +C -

A:

Q: 5. Find y' by Implicit Differentiation for * 2y — Зу? + 4х y' = - 1 y' = 3y – 2 %3D 1-3у O b. a. 1 1…

A: Find out the implicit differentiation of given function.

Q: x + 2 а. x +3 х — 2 b. x +1 х — 2 с. x +1 x – 2 d. x +3 11. What iss in terms of t, if and 4r 5t 22.…

A: According to our guidelines we can answer only first question and rest can be reposted.

Q: lim х-2 x→2 Vx + 7 - 3 Score С. 1 А. 6 В. 4 С. 2 D. 0

A: As we can observe that it is an indeterminate form(0/0). To solve the limit, multiply and divide the…

Q: 1-2lcoel+)-¹ = (1+¹+¹+) {¹+3 +.. ***

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Q: 6.)f(x) =- 3x + 7 g(x) = 2x - 8 Find (gof)(x)

A: Since you mention that : answer for number 6

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.