Solue u (x)= (x-1)e+4 ult)dt e.

Q: Scosh(2tn(x)dx

A:

Q: Find f(x)

A: It is given that f'x=1+3x, f4=25.

Q: e 3x dx ex-1 X .

A:

Q: e1 dx 1 e O (e-1 )/e - 1 1 ООО О

A:

Q: part ii, thank you very much.

A:

Q: f(x)% 3D tanh In(2x) is equivalent to

A:

Q: If ƒ(x) then f"(x) = · = 0 X (t³ + 5t² + 1) dt -

A:

Q: find y' (xy)x = e

A: Given problem:- find y'   (xy)x = e

Q: (B)(10M) Evaluate (y(x)) dx y(x) = cot (csc(sec(In x))) %3D

A: derivative

Q: Find linearization of the given function: f(x) = 1/x at x=0.5, dx = 0.1 %3D

A:

Q: Find dy/dx if f(x) = csc (x³ + x + 1)

A: Derivative of the function

Q: Find f′(x). f(x)=5x4 ln x

A:

Q: -g(x) = x²sinx cosx . Find g'(x).

A: We will use the product rule of differentiation to find the derivative.

Q: F(x) = 9t dt

A: given: Fx=∫0x29t dt Fx=∫0x29t dt=9∫0x2t dt=9t1+11+10x2=9t220x2=92t20x2=92x22-02=92x4-0=92x4

Q: Solver: y(ln(x))dx+(1+2y)dy=0

A:

Q: e"(cosh(2t)-cosh(5t))dt = ? -St

A: We will evaluate this integral using Laplace transform definition.

Q: f(t)=ln(ln(6t))+ln(ln2) f′(t)=

A:

Q: S (8)0.5x dx 2

A: Consider the integral as, I=∫2480.5xdx Simplify the expression as,…

Q: Let f' (t) dt = 9 and f (2) = 3. Find f (6).

A:

Q: Find h'(t) if h(t) = %3D t1/2 1617 h'(t)=

A: Given:

Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: Find f(2) if f (x) = e"

A: given equation f(x)=ex

Q: 4. F(x) = (1- t) dt %3D 4

A:

Q: Find y' if y = (2x + 1) (4x – 1)². %3D

A:

Q: solve dx dt. (1 = 72 X -2 7 with X (0) = 3 L2

A:

Q: Find f. (x + 1) f'(x) = (1) = 3 %3D f(x) =

A:

Q: If f'(1) = 3e2 and f(0) = 2 then find f(1). %3D %3D

A: Given:     To determine: f(1)

Q: х (1 point) If f(x) = t' dt %3D then f' (x) = f'(-5) = %3D

A:

Q: - If g(x) 1 dt , find g'(2). 4 +t

A:

Q: t (x) = e – 3x +2 | Find Where Increasing/Decreasing

A:

Q: (e* + 1)ydy = (y + 1)e*dx

A: Given differential equation is (ex+1)ydy=(y+1)exdx⇒ydyy+1=exex+1dx⇒1-1y+1dy=exex+1dx

Q: 1 (x2 5)e-X dx

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.