1 Given that L-(4+9)) = 8in(Bt) – sin(Dt) L-'(+4)(s²+9) Match the following values. 10 is the value of Choose. 15 is the value of Choose.

Q: If F(x)=sin(7-x5-13-x³ +5-x). Calculate dF(x) = dx

A:

Q: 05 y' + (cot x) y 3 sin x cosx

A: We have to solve the given differential equation.

Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: *T/4 sec² xdx 26. 27. sin xdx TT 28. COS xdx

A:

Q: x+(1/x)=2 cos theta , then show that x2+(1/x2 )=2 cos2 theta

A:

Q: cos( 2 sin1 (X/17)) = Select one: O 2x ( 289 - x )o./ 289 O ( 2x - 289 )/289 None O 34 x/( 289 + x)…

A:

Q: find the first and Second derivatives of the equation fon = Sin [√sex+x³²e² 3 SX X. C tanx J-ex

A:

Q: -1 (3) cscx = sin X

A: We have to use proper substitutions and properties of analytic function.

Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: C- Find f' of the following: 1) √2x³-2² + In ² 2) 3xe³r+1 3) sin ¹(³).

A:

Q: solve for y'. y=sin-1[(ax+b)/(bx+a)]

A: Sin-1x can be written as asin(X)   So we have expression as y=sin-1(ax+b)(bx+a) We have to solve for…

Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

A:

Q: Solve cosx dx + (sinx)y=1 Select one: O ay sinx + ccosx O b. y = 2sinx + 2cosx + c O c. y = sinx –…

A:

Q: If f(x) = sin?x, then f"(x) = %3D A 2cos2x B cos2x -sin2x D -4sin2x

A: Given, f(x) = sin2x For the given function , applying chain rule ,  First differentiate it as { xn ,…

Q: etermine the form that would make f sin () cos () sin(0) de

A: We have to determine the form of the given indefinite integral

Q: Evaluate sin (ax) (ax) V3 (2ах) da Cos

A:

Q: Evaluate * sin (x²) dxdy y

A: The integral is bounded by the curves: x=y,x=π,y=0,y=π The region is as shown below,

Q: Isin ( 3x²+5x+2)'-

A: Formula used:

Q: 3. √9-x2 dx (hint: sin x = S dx (hint: sinx = (sin²x)(sin²x)) x4

A: