cos(2t) dt y = 200 (c) Suppose a friend finds a genie and is given three wishes. They wish for money and a car, but for their last wish they ask for the antiderivative of sin z cos z. The genie writes in the air | sin(z) cos (z) dz = - cos (x) +C 3 and then disappears forever in a cloud of smoke. Use the second part of the Funda- mental Theorem of Calculus to find the exact area under the curve of sin z cos²x over the interval (0 z)

Q: (b) sinr + cos² y 4 P(품,등) 3

A:

Q: Part A (i) Let f(x) = ln(3ª + 8"). Find f'(x). %3D (ii) Find 2" cos(r)` cos(2") d da

A: Derivative of function

Q: 1 Laplace transforms Calculate the Laplace transforms of (i) H₂(t) cosh (3t), where cosh (at) = 1/²…

A: Solution: (i) let, f(t) = H2(t)cosh(3t)                   = H2(t)[(1/2)(e3t + e-3t)]…

Q: Four equations are provided below. Which equation follows from the Power Rule? I. (P)' = pr P 1…

A: Answer is option (a)  Because only equation 3rd follows the power rule .

Q: How can I find the dependent variable, independent variable, order and linearity (whether linear or…

A:

Q: c. _h(x) = e¯³(sin(x) + 2x); only quotient rule

A: To solve the following using quotient rule

Q: Let A = ° -2 [23] eAt = e2t T eAt = e³t eAt = e³t e³¹ = cos(3t) [- sin(3t) cos(2t) sin(2t) [ e37 .…

A: A square matrix A is given. The objective is to find the value of eAt. If A=a-bba, then eAt=eatcos…

Q: f(x) A B = arcsin x, then lim 1/1/12 0 ㅠ 6 f(x)−ƒ( ² ) X→ X- 1|2 is

A:

Q: dx x4+16 Įtan-( x2 + c 4

A: Given that, ∫xx4+16dx

Q: sin(x + y) = sin(x) cos(y) + cos(x) sin(y)cos(x + y) = cos(x) cos(y) − sin(x) sin(y)23a. Find an…

A: The objective of the question is to find the exact value for sin(75 degrees) using the given…

Q: (c) f(y) = √√2y + (3y + 4y²)³ 1-t (d) g(t) = sin³ (e¹−t + 3 sin(6t))

A:

Q: sin(2t). Find Əz Ət if z = √r² + s², r = cos(2t) and s =

A:

Q: [4] Let f(x) = -p³ Position to find p2, P3, and p4. cos x and po = -1, pi = 0. Use the Method of…

A:

Q: You can use the Law of Cosines (see Figure 3.41) to find an equation that relates and 0. Figure 3.41…

A:

Q: Find (a) sin(?) and cos(?), (b) tan(?) and cot(?), and (c) sec(?) and csc(?). Assume x = 7, y = 9.…

A: First we shall solve the given trianlge. Now we shall find the third side using pythagorus theorem.…

Q: You are given that h (x) C = dh dx for a number c. You have to find c. = 6 sin (7x) + 5 cos(7x) 3…

A:

Q: What is the equation of the graph below? (x.0) (22.-2) O y = sin (2x) - 1 %3D O y = cos (2x) - 1 O y…

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.