1. The derivative of the sum or difference of two differentiable functions is to the sum or difference of their derivatives. 2. The derivative of a is zero. 3. In the Power Rule, we subtract in the exponent. 4. If flx) and g(x) are both differentiable functions at x with g(x) # 5. The derivative of 9 is

Q: Q2) Solve the D.E xdy + (2y – x* + 3x)dx = 0

A:

Q: +0 (2х — 1)" n V4n + 1 n=0

A:

Q: 8. [sin? x cos' x dx Ssin*

A: (8). Given: I=∫sin2xcos5xdx   As we know from the trigonometric identity; sin2x+cos2x=1 And The…

Q: lim (sin r)tan z T/2

A: Given problem :- Identify the indeterminate form and evaluate limx→π-2sinxtanx

Q: sin (t) -dt 3 (4+ cos (t))?

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Solve for the following integral: 1 -dx (e2x – 4)5/2

A: I=∫1(e2x-4)52  dxu=-2xdx=-12 duI=-12 ∫due-u-452v=e-u −4dv=-e-u du-dv(v+4)=duI=12∫1v52 (v+4) dv

Q: 4. E+sec"x+1\dx

A: Solving the problem by finding the value of the integral.   NOTE :: As per our Expert guidelines we…

Q: f(x) = x²+2x+1 g(x)= x+3 Set up the integral to find the area between the two curves. 1 -3 -2 -1

A: We have to find area bounded by the given curve.

Q: Consider the function f(x) 5x + 1 (a) Find the Maclaurin series of the function f(x), stating your…

A: Let's find.

Q: Determine if the improper integral converges or diverges. If it converges, find its value. In dx

A: Here we have to integrate the given problem.

Q: 4. A1 y = 2x 2+ A1+ A2 = A3 1+ y= x2 482

A:

Q: Find Duf at P. f (x, y) = 3(4 +xy)2; P(4,3); u = 1 i+ j NOTE: Enter the exact answer. Duf

A:

Q: + inf 1 Σ п2 — Зп + 2 n=3 W

A:

Q: Find the antiderivative of the functions. S 6x dx S(12x - 5)dx S 3dx S(2x2 + 3)dx 1.) 2.) 3.) 4.)…

A: 1. ∫6x dx2. ∫12x-5dx3. ∫3 dx

Q: Use the 3rd Degree Maclaurin polynomial for g(x) = x COS to approximate the value of 0.2 cos(0.1).…

A: We have to find 3rd degree polynomial for the given function.

Q: Q4) Find plane area inside the polar function r = 2 and outside the polar function r = sin (-0) +1…

A:

Q: (-1)" V2n² + 5 Given: power series > (x+ 1)" n=1 i. Determine if the resulting series of constant…

A:

Q: (-1)" V2n2 + 5 n er series (x + 1)" n=1

A:

Q: I 3n O The region bounded by y = sin x and x- axis on the interval [-

A:

Q: Given cos(x) = (-1)" n=0 (2n)! -x2n for all x ER, Express the integral cos x dx as a power series.

A:

Q: 1. Evaluate the integral. -1 (6х — 12) dx

A: To evaluate the given integral.∫3-16x-12 dx

Q: If substitution technique is used to solve the integral [(12.x+3x* )(10x² +x³ – 2)° dx then the…

A:

Q: +oo (-1)"n" sin" () ' Σ 2n n=1

A: According to question,Given series,∑n=1+∞-1nnnsinn1n2n

Q: Given: a, = In(n + 1) – In(n) for n e N Determine if the following is convergent or divergent. (a)…

A: Given that an =ln(n+1) - ln(n) We have to find whether the sequence ann=1∞  is convergent or not. A…

Q: Determine whether the following converges or diverges. 2n + 1

A:

Q: sin x Let g(x) = . 1 Find the derivative a'(x). dt . 2 1+t3 cos? x 1+ sin x sin x 1+ cos³x cos X 1+…

A:

Q: d -sin 6 if0 is given as dx What modifications would have to be made to find the derivative an angle…

A:

Q: EVALUATE THE LAPLACE TRANSFORM OF THE GIVEN FUNCTION USING APPROPRIATE THEOREMS. f(t) = t? cos 2t.…

A: Answer is in below steps.

Q: бх — 8г2 — 5 dx (2л — 1)(4г2 + 1) -

A:

Q: { II. Consider the sequence í n+ 2)! J n=1 a.) Show that the given sequence is monotone. b.) Use the…

A: Here, the given sequence is: πn(n+2)!n=1∞ Let, an=πn(n+2)!

Q: (2 tan¯'n – T)

A:

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: 5. What is the derivative of 2x*? A. 8x3 В. 2 С. х D. 0 6. Consider the function f(x)=|x-21 at x-2…

A: Since you have posted multiple questions i can do first three question as per our company guidelines…

Q: VIII. Use the 3rd Degree Maclaurin polynomial for g(x) = x COS to approximate the value of 0.2…

A: Third degree Maclaurin polynomial of a function f(x) is given by,…

Q: Calculate the moments My and My and the center of mass of a lamina with the given density (p = 3)…

A:

Q: Answer: dy = 3yCx'ty)

A:

Q: A(-4, 4), B(12, 12), and C(16, 0). Medians CD, BF, and AE are drawn. dians of triangle ABC are…

A:

Q: TOPIC/S: Trigonometric Integrals Evaluate: x? 1. dx (x2-25)2

A:

Q: ind the sum of the convergent series. +00 3n+1 Z 6n-1 n=0

A:

Q: Integral

A:

Q: 0 e1/x dx

A:

Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: Using homogenous differential equation determine the particular solution of xy?dy - (x³ + y³)dx = 0…

A: differential equation

Q: Q: Evaluate the following integrals: (10 dt, 10x dt 1. 5t re dx 2. J0 x(Inx)?

A: Question 1,Given,           ∫510dtt+∫5x10xdtt

Q: x² dx J (² – 25)5/2

A:

Q: Consider the parallelepiped with adjacent edges u = 3i + 3j + k v = i+j+ 8k w = i+ 9j + 5k V Find…

A: Given;  u=3i+3j+k v=i+j+8k w=i+9j+5k.

Q: If uxv=uxw, u 0 then O None of the choices O v=w+ ku u=v+ kw O w=u+ kv

A: Let a→ & b→ be two non-zeros vectors. Then a→ & b→ are parallel if for some scaler k we have…

Q: Given the integral of S cos² x dx,

A: O integrate the given function.