EX Show that J (x) =2 sin X zm + Sali-J Cx)= L m + X4 /2 L2)(1)(E 2 (2!) Y2) 4 112 2.

Q: Q3. Solve in terms of Bessel's function, the ODE: x²y" + xy' +((inx)² +) y =0 z=lnx using a Rule…

A: Here, x2y''+xy'+lnx2+14y=0,  z=lnx.

Q: Q7/ Express in the form x +jy (1) e(r/2-j) (2) In(3 – j) (3) sin(t/4+ j2)

A: (1)  ejπ/2-j=ejπ/2-j2                =ejπ/2+1                                         j2=-1…

Q: 4. Find (f-1)'(1) if f(x)=x' +8x+sin(3.x) а. Find (f-1)'(2) if f(x)= Vx' +x +xr+1 b.

A: To find the derivative of the inverse of a function

Q: 2) i)' If 1 [ f(x) f(z)dz = 6 ln(|z|) sin(z) - 3e³ +2². then find f(x). ii) { Evaluate se - r² + 16x…

A:

Q: If f(t) = e-t3 – 2 sin 2t determine L{f" (t)} %3D

A: Formula Used: L{eattn}=n!(s-a)n+1L{sin at}=as2+a2L{f''(t)}=s2L{f(t)}-sf(0)-f'(0)

Q: (1) (II) 10 F. 10 +t 10 10 -10 -10 (II) (IV) 10 10 斗t 10 t 10 -10 -10 a) y = 10e-t/2 cos 2nt b) y =…

A:

Q: PLS HELP ASAP ON ALL

A: 4. Given:f(x)=π2Getting the derivative, we have:f′(x)=dxd​(π2)Since π is a constant, the derivative,…

Q: 1 dx V9+8x – x2 Evaluate :

A:

Q: 3- 2 -3 2 -1 2 3 g(x) = sinh(x) -1 -2

A: the symmetry used here is the y-axis which divides the graph into 2 equal portions.  the graph given…

Q: show that | | J.(x)dx x² J,(x)dx = x²J¼(x) + x J,(x) – %3D

A: Apply the integration by parts method and use the identity ∫xpJp-1xdx=xpJpx, to evaluate the…

Q: A 2xe ²x² B Xex² Ⓒ2e+² D 2xex² Let f(x)= ex², find f'(x)

A: given  f(x)=ex2d dx(ex)=exd dx(xn)=nxn-1

Q: B. Find f(x) if f

A: Solution of the problem as follows

Q: -1 Ax) = 7xsin (x) f'(x) =

A: SOLUTION-

Q: f (x) = { ₂x² (²/²) ² 2=1 Coso f(z) dz= ? 23

A: We have to calculate

Q: Suppose f (x) = dr=AV5- 3x +C, for constants A and C, what is the value of A? %3D If V5- 3x

A: Integration

Q: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

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Q: What is r' (x) when r(x) = In (x³ + 2x2 + 3x +1)? Select the correct answer below: In (3z2 + 4z + 3)…

A:

Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: 07/ Express in the form x + jy (1) e'(x/2-j) (2) In(3 – j) (3) sin(r/4+ j2) -

A:

Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

A:

Q: Find the function f(a) such that f'(x) = 5 sinh(x) – 2 and f(0) = 4. a) O f(x) =-5 cosh(x) – 2 z - 1…

A: Given that f'(x)=5sinh(x)-2 and f(0)=4 To find the function f(x)

Q: 22. Find f/(x) and simplify 1 -1 a) f(z) 3-52+1 3 b) f(x) 1.8Vc) f(x) = 32

A: Given, functions