Question 1c) i) Given the quadrature formulae, ,3 | f(x)dx = h[ny, + Ayo +5 23 A²yo + 6 4 n³ + n² ) a³yo + .…] 2 Explain why, Explain why, f(x)dx = h[y, + Ay.] at n = 1 and not, S* f(x)dx = h[yo +Ay -A³yo] from above %3D 12

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

Q: 10. Determine dy of y = 5-2x+7 dx In 5 -2(5-²x+7) ○ (5-2x+7) In 2 ○ (5-²*+7) In 5 ○ 2(5-2x+7) In 2

A:

Q: xe* dx (x + 1)2

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: 4). 2 ava-1 3). S sech-x tanh;x dx 2 2 6). S csch* 2x dx 7). S x² sech x³ dx

A: Since  we are given with the multiple number of question and our guideline is solve first question…

Q: 1 2x Evaluate [(4x-7)ay dx.

A: To evaluate: ∫01 ∫x22x (4x−7)dydx Let I=∫01 ∫x22x (4x−7)dydx First evaluate with respect to y taking…

Q: 2) Find the derivatives of a) y = 7 - 6x-x² b) y - ³x 8 √x

A: Given :(a)y=7-6x-x2(b)y=-8x

Q: Finds 2) S 12x-31 dx

A:

Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: f (x) = [x + 4] df 1 =? dx 8 - O A) 1 В) 10 о с) -1 D) 2 O E) 0

A: The function f(x)=x+4. We have to find dfdx12=?

Q: True or false: True False d dx 2 + ² = 1/2 2+ - X

A: d(xn)dx=nxn-1d dx(constant)=0f(x)=2+1x

Q: Evaluate: d dxJ (21² + 5)² dt.

A:

Q: Provide an appropriate response. Is 4x(4x+ 1)3 dx <2(4x+1)4+C? A) No Yes B.

A:

Q: - 4x + 30 -dæ Evaluate (x – 5)(x + 5) + C

A: To solve the given integral first break the integrand into the simple expression using partial…

Q: Use u-substitution for #7 xe* dx

A: Substitute:-         x2 by u then integrate

Q: (c) Find the value of √a²-x² Sa giving your answer in terms of a. 1+ 2(x + y) x² + y² dx dy,

A:

Q: Differentiate. f(x) = In (4x+5)(x+8)5 (1-4X)6

A:

Q: dy 3) Using the function y=f(x)=x², state which of the following uses of the notation: dx d and are…

A:

Q: b) if J(zf64)} - 39ga) ) ce = Sin () %3D and S(3f (x)+9 6)) dx = tan () 2. 2. +596)) dx

A:

Q: For the function y = x² + 2x, the value of dy when *=3 and dx=0.1 js -0.15 A) 0.15 B) C) - 0.8 0.8…

A: We will find out the required value.

Q: B. Using Change of Variables and Generalized Power Formula, integrate the following: 1. fx (x2 –…

A: Since we have multiple numbers of question and our guideline is solve first question and kindly…

Q: dy Find if dx (² + 7)* 3 5,

A:

Q: Find given that y=[atan-¹(bx)]². dy dx Assume a,b ER. 2[atan-¹(bx)] O 2[atan-¹(bx)]- O 2b[asec²(bx)]…

A: To find dydx given that y=a tan-1bx2.Assume a, b∈ℝ

Q: Differentiate these using the product rule. Write your answers in fully factorised form with the…

A: NOTE According to our guidelines we are supposed to answer only one question and three subparts.…

Q: sinh x 20. 1x1-3 A) 2. B)-2. D) 0.

A:

Q: 1. Find dx dy for the following functions: 1) y = (x- 3)(1- x) (ans.:4 - 2x) b (ans. :-,) x* 2) y=…

A:

Q: (a) Find S 1+ (x + 2)² dx and 1+ (x + 2)² dx.

A: Concept: Integration: The summing of Discrete Data is indicated by Integration. To determine the…

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.