Sin[t] 2) Suppose a 3D motion is given by X[t] = Cos[t] t-2) Find a time when the speed v[t] is not changing, E = 0 @ t = a) 0 b) 1 c) 2 d) T/4 e) T/2

Q: y = In x3 sinx 2 Cx² + 4

A: The function is given by y = lnx3sinxx2+4 To evaluate: The expression of dydx.

Q: find sin (x) Given tan(x) and x E 5 a) b) V41 4 d) 41 c) া Ln

A:

Q: 3. Compute : exp (sin (e).

A:

Q: Pr. #14) Find and sketch the domain of the function in R2. In [sin- ()] (x, y) x2+y² %3D -

A: This is the problem of multi-variable functions.

Q: Find f. f(t) = f"(t) = 7et + 3 sin t, Need Help? Read It f(0) = 0, f(π) = 0

A:

Q: A unit tangent vector to the curve r(t) = [sin(t), cos(t), 2f] at the point A:(0, — 1, 2п) is given…

A:

Q: Suppose that r(t) =. Then the speed is

A:

Q: 2. In the following cases, express the f(t) as a single sinusoid: a. f(t) = cos wat - √3 sin wat b.…

A:

Q: Evaluate . 2y2 cos(x) dx + 4ysin(x)dy where C is the line from (0,0) to G,0) and then a line from (,…

A: Line integral over the curve.

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Sin(t) Find S'and S" for the function: S + t2. %3D t

A: Differentiate

Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

A:

Q: Find f. f(t) f"(t) = 2e + 3 sin t, f(0) = 0, f(π) = 0

A:

Q: Calculate :| t' sin(t) dt [Hint: At some point in the solution, it might be helpful to write t as t2…

A:

Q: Note: You are attempting question 8 out öf 12 The function (z) that is harmonic outside the unit…

A:

Q: A particle moves along a line so that at time t, its position is a. When does the particle change…

A:

Q: if z = cos20, and 0 = [cot(w) + 1] - %3D rcotx sint Find if cot?y = x² + Sy2sinx dx

A:

Q: JA particle moves in astraignt line andl has acceleration given by a (t)=2 sint + 3 C0st. It's…

A:

Q: (b) (sin 0)y"+ (0+ cos 0)y" 2tan@

A: Given: sin θy'''+θ+cos θy''=2 tan θ (a) The number of the highest derivative in a differential…

Q: For F(t) = (3 cost, 3 sin t, 4t) find T,Ñ, and B

A: Given that : r→(t)=3cost,3sint,4t. Therefore, r'(t)=-3sint,3cost,4. So, r'(t)=9+16=5. Therefore,…

Q: 4. Determine the phase shift and the vertical displacement with respect to y = sin x for each…

A: Given problem:-

Q: 1) Let 7(t) = (t, 2 cos t, 2 sin t), -4 <t< 4. Find the length of the curve.

A: In

Q: The curves F₁ (t) = (2 sin(t), 4 cos(t), e7t) and 72(t) = (3 ln(t), 4√t, t³) intersect at the point…

A: The angle between two curves is the angle between their tangents at the point of intersection .

Q: Suppose z = f(x, y) = (x² + 2) sin(y) + xy². By setting one variable equal to a constant (either x =…

A: Given surface is,This equation represents a surface in three-dimensional space.To find the:

Q: Find for the following functions: - dx 1) y = (cos x)V 2) y = sin x* + e!nx 3) y = 7cos/2x+3

A:

Q: Use the convolution theorem to show that cos T sin (t – T) dr 1 sin t. %3D 2

A: Convolution theorem use integration of product of 2 functions and transforms them to pointwise…

Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

A:

Q: Encuentre TLt), NCt) B (t) de cLE) = ( cost , sent, t)

A: We will use the respective definitions.

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.