Compute L(f(t)) 13. L((t+1)²) 1. L(2t) 14. L((t+2)²) 2. L(4t) 15. L(t(t+1)) 3. L(1+2t + t²) 16. L((t+1)(t+ 2)) 10 4. L(t² – 3t + 10) 17. L(E t" /n!) 5. L(sin 2t) 18. L(10 tn+1/n!) 6. L(cos 2t) 10 19. C(Σ sin nt) 'n= 7. L(e²“) 8. L(e-24) 20. L(En=0 cos nt) 21) e{ cos(au) – cos(bu) dpu 9. L(t + sin 2t) 10. L(t – cos 2t) 11. L(t+e2t) 2. L(t – 3e-24)

Q: x²+1 Find J+3x+1 11.

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Q: S x4X+1 2

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Q: Differentiate and simplify: y= (3 – 4x)²* O a.y' = - 2(3 – 4x)²*-4x + (3 – 4x)In(3 – 4x)] Ob.y'= 2(3…

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Q: (x? - 1)² dx = x$/5 - 2x/3 + x + C Select one: O True O False Jdx/(1 - 2x) = 1/2 In|1 - 2x| + C…

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Q: S(x + 1)(2 – x)° dx 7(2 - x)* - (2 - x)* +c 7(2 - x)* -(2 – x)* +c 3. (2 - x)* +(2 – x)* +c 금(2-x)*…

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Q: Find *: (a) 4x°y³ + 2x³y-y-2x-4 0. %3D

A: Given  4x5y3 + 2x3y - y - 2x - 4 = 0 We have to find dydx.

Q: S Sifoo-gool dx O d2 (f.g) = Sup {/fox) - gox|} V£₁9 € [0₂4] if d, (fig) = Find Ⓒd₁ (√x,x) @d₂…

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Q: if y+z=10, then (10x+y)(10x+z)=100x(x+1)+yz?

A: It is given that y+z=10. Use multiplication of binomials to find the value of the following:…

Q: Differentiate. f(x) = In In dx (5x + 2)(x+7)3 (1-6x)6 (5x+2)(x+7)3 (1-6x)6

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Q: pk Ph (x)=k! T(m-k+1) (k+m+1) m X \x X

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Q: d2/dt2 (21t)

A: In general the second derivative is used to find the acceleration of an object . The second…

Q: (b) (x*y2,1/3(xy) -1/3 X + 0, y # 0

A: We will simplify the expressions by writing the exponents with equating the bases.

Q: 6. (a)f dx x(x +3)2

A: To evaluate the given integral

Q: g(*) = ln (-3x+11) %3D calculate (X), A) 2(-3r +11)-3 B) -3(-3r + 11)-1 C) -54(-3r + 11)-3 D) -9(-3r…

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Q: 시e (+-2) u(1-2) T 2-7

A: Some of the proprieties of Laplace transform Lu(t-c)g(t)=e-2cL[g(t+c)] Ltneat=n!(s-a)n+1 Leat=1s-a

Q: Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x^2 + 1. Compute the following: A. f(g(-3)) B. f(h(7))…

A: I have given the answer in the next step. Hope you understand that

Q: + 9x + 27 dx (x + 3) (x² + 9)

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Q: evaluate L-1 { t/(s-2)(s+3)}

A: By using partial fraction and table of Laplace transform we solve the given problem as follows :

Q: In (x²) esin(2r)

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Q: find the value of x in (1/(3x+1))+(1/(x+1))=(1/(3x+1)(x+1))

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Q: Yob) a) fog)(x) & 3. = (x)) JI 2. x+2 (x)6 8 %3D then find

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Q: If y=(X+3)(X-5)^7 then find y`

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Q: [(*+4) - 8]* dx 32 (*+ 4 )3

A: The given integral is 32∫0∞x+4-82x+43dx. Evaluate the value of given integral.

Q: 2x+6)dx x²+2x+5

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Q: る(4xナx)(10x2+x2-2

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Q: (xdx ydy + zdz)2z {(z²x²y²) (xdx + ydy + zdz) dz + %3D

A: Differential equation

Q: Si dx 2 x² - 4x+8

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Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)

Q: • N/W [ (x³-3x) dx - 1

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Q: √(x + 3) dx √16-x²

A: Solution

Q: solve 19. (5x' + 4x? – 3x) – (x² + 7x + 2) 20. 3(x – 1) + 4(x + 2)

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.