(a) L{t°e=5t}, (6) L {e-t cos 2t}, (e) L {Vi e}, (d) L {e-8:/VE}. Find

Q: ei=e*(cos(y) + isin(y))

A:

Q: Q4// Find the value of csc(sec-1 2) + cos(tan=²(-V3)).

A: Here  given as Use some trigonometric formula as

Q: θ = cos^-1[sin(LT1) sin(LT2) + cos(LT1) cos(LT2) cos(LN1 − LN2)] How does this formula go with…

A: Consider the figure as our Earth. O is the center of the earth Point P on the earth surface has…

Q: If cosecant(x)=8, for 90 degrees<(x)<180 degrees, then what is sine(x/2), cosine(x/2), and…

A:

Q: e* secʻ(e* +1dx tan(e* +1) 8. 2x² – 7x -5 9. 2x+1

A: 8) Consider ∫ex sec2(ex+1)tan(ex+1)dx                       (1) Let tan(ex+1) = t On differentiating…

Q: Solve dx dy for y= sec (In x) In (tan x)

A:

Q: 8 EI+(-1)] = i=1

A:

Q: Solve d²y dx² cot x dy - sin² dx sin² x.y = cos x - cos³

A:

Q: sect (x) dx[ by two methods

A:

Q: (a) y = In(sec²x) (b) y ecos + cos(e) x² −1+2 (c) y = x (d) y = sin² (e) y = (f) y = (cos(√sin(x)))…

A: Let's consider  the properties of differentiation.Let f(x) and g(x) are two different function…

Q: d? -(sin-'(x²)) dx2 2– 4x4 A 3 2– 2x4 B 3 2+2x4 3. 2+4x4 D

A: Here we have to use the concept of derivative

Q: what is y' of y=sin-1(cos x)

A:

Q: 음 (sin-" (2))\_-+ = (교2)) | dx 2(:) A 1+ 2() B (C 2 (4) cos-1 (16) D -2 (금) cot () csc(6) CSC

A:

Q: T/4 (b) 4 sec (0) tan(0)dө.

A: Answer is- 4(√2-1) Explanation is given below...

Q: csch (2 sin2x) dx 1. V1-4x² r(²-1)cos[cosh (In r)]dr OS 4.

A:

Q: e² tan (e²) b) dr I sec2 (e-) – 7

A:

Q: V3 sin

A: We use Trigonometry table to find out these inverse values

Q: 3. arcsin (cos A 3

A: Consider  arcsincos5π3

Q: sec? (1/x) dx. 9: (16pts) Evaluate

A:

Q: 2, " cos“(x)sin*(x)dx

A: To find : ∫0π2cos6xsin4xdx

Q: 는(csc-1(324)) = d SC dx

A:

Q: dx

A:

Q: (a) Find: L{(e + e*)?} -t (b) Find : L 2+11 } 2s (c) Find: L{421

A: a) Le-t+e3t2Le-t+e3t2=Le-2t+2e2t+e6tF(s)=Le-2t+2Le2t+Le6tF(s)=1s+2+2s-2+1s-6F(s)=1s+2+2s-2+1s-6

Q: sin3 x dx (③)글 4 () (0)

A:

Q: dx Evaluate V- x² – 4x – 1

A:

Q: f'(3i) = -i, g(7+ 2i) = 3i, g'(7 +2i) = -4. Find (f o g)'(7+2i). 4i -4i 2.

A:

Q: Evaluate les-). d 3x dx OA (3x³- x?)e3x²-x?-1 O A. ² – x² – 1 OB. O B, e oc (9x² - 2x)e³x³-x? OC.…

A:

Q: 13T (b) sin-(sin(- -)) = %3D 11

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.