The Laplace transform of L[eH sin h(3¢)] is_ 7. (a-7)2-32 3. (*- 7)ª - 37 3. (-7) - 7 (-3)a – 3a

Q: Q4) Find Fourier transform of the functions: 1)f(x)= nxl, x π 3)f(x)=xe-x1, x ER 2)f(x) = 4)f(x) =…

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Q: then prove that i) F, [ƒ (x) cos ax] = [f, (p + a) +f, (p a)] 1 ii) F.[f(x) sin ax] 2 [f. (p + a) –…

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Q: S Q16) L−¹ {(8 − 1)² + 4) (A) et [cost + sin t] (D) et [cos 2t+sin 2t] (B) et [cos 2t + sin 2t] (E)…

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Q: tan (3r) dr = a tan(3x) – In(v1 + 9x²) +C 3 a tan (3x) + In(v1+9r²) 3. e tan '(3x) In(v1 - 9x² +C a…

A: We know that, from basic integral formula ∫tan-1x=xtan-1x-12log1+x2+C          ⋯⋯1 We have, the…

Q: e> and deduce that Find Fourier sine transform of- ar e bx e | sin px dx = Tan2 - Tan a

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Q: Find the vertical asymptote(s) of f (z) = %3D 23-4r Section 3.4 O = 0, r = -1, r 1 O y = 1 O = -1, =…

A: The given function is: f(x)=x3-xx3-4x

Q: To find the Laplace transform of e^(6t)cos(at)you would substitute  into s/(a2+s2) which gives ?…

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Q: (3) Prove that n=2²°² is a square. 2K+1 where K = 1 $ (n)

A: This follows from the definition of euler Phi function

Q: (4 -3) Please show all working 9. -2 (1) Given that P = 2 ) and Q = ( %3| -3. 4 -3. Calculate: (i) P…

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Q: 110. π/3 -π/3 /sec²x - 1dx

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Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: -5 -4 -3 -2 -1 1 2 3 4 5 At the point shown on the function above, which of the following is true?…

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Q: Read each of the two statements carefully. Choose A(if both statements are true), B(if the 1st…

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Q: 37nx Find C2{sin (*} (Finite Cosine transform) O A. 6L O B. 4L - 5TT OC. 2L - 5T O D. O E. None

A: Find C2sin3πxL

Q: Question 4. Using the Mean Value Theorem, prove that (a) 1 1 dx < 1. a2 )5 32 (1 + (b) 4 < Vx2 + 3dx…

A: Given,a) to prove132≤∫011(1+x2)5dx ≤1mean value theoremIf 'f' is continuous on [a,b] then there…

Q: Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0

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Q: 8 3 Find the Inverse Laplace Transform of- + 3s2+ 12 s2– 49 3 4 A) - sin2t + -cosh ( 7t) 7 3 4 –…

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Q: k ak ak a-1,a +1 (-1)* 1/½(-1)*+1 kak 4), a +1 a- (ak + b)(n) (ak+b)(n+1) a(n+1)

A: ∆ak= ak+1-ak      = ak(a-1) therefore anti difference of ak=ak/(a-1)

Q: Find L- 26 2s-18 e-9t 26 -9t O 26et

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Q: Evaluate L{3(sin² 2t )} 24 24 24s 24 а) s(s² + 4) b) d) s(s² + 16) s(s² + 16) s(s² – 16) a O Option…

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Q: 5. Find dy dx of √xy + 2x = √√√y

A: Topic = Derivative

Q: 7) Chapter 2.6 Find the first four derivatives of f (x) = 6æ³ – 2x² +1

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Q: O Evaluate (u) B(3. 5). (b) B(3/2.2). (c) B(1/3. 2{3).

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Q: afdæ dx Find + C

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Q: (x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

Q: The function f(x)=/25-x' is contionous on

A: It is continuous function.

Q: 1. L{sc" sin wt} L{e* (acost+6 sin t)} -kt cosh 2t +-sinh 2t 2 3. L 2.

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Q: 5 [x²² sec (2) com ³ (2) abr dx 7 2tan can ²2 ( 1 ) [7tan² ( 1 ) +1 + C (Α 77 11 7 2x + (-) == ² (7)…

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Q: 15. (a) (i) Find the Z-transforms of cos and 'n(n+1) no A (ii) Using convolution theorem, evaluation…

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Q: L{3e' sin(5t)} 15 +25 52+25 (8-1) +25 15 $2 28+26

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: