Approximate sin by using a linear approximation with f(x) = sin x. %3D 13 sin = f(a) + f' (a)·h = c, where 13 a = h = C = (Note that these are numerical answers. No letters can be used in an answer.)

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: How to compute Cp using below equation, OP, sin 0; Cp, = 2 sin? 0; +2 cos 0 dy dy Where y = 0.5x…

A: To simplify: CPi=2sin2θi+2dθdyisinθi∫0yicosθdy

Q: 5 dx Find dx, x> V25x? -9 5x In 25x2-9 + C 3. sin-13x+c 1+9x2 +3x|+c 1 V1+9x? + C 3x 3. + C V25x2 -9…

A: The solution is given below in the next step:

Q: 2 sin (t) cos (t)d J

A:

Q: " , [sin(Inx?)]²dx Which of the following is equivalent to sin(Inx 14) dx sin2( Inx 14) dx B ©…

A: The given integral,       ∫sinlnx72dxx

Q: dy of the following. dx A. Find 1. y = (sin* x²)[sec(Sin-1 x²)]

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

Q: IV. Integration by Parts 1. | sin x sin 4xdx

A:

Q: x² – 1 Consider solving dx using a suitable trigonometric substitution. After performing…

A:

Q: dx Find given, dt (a) 1 + sinx = 9t, (b) 12 cos 12x-= 10, 1 (c) tan x = (e) tan 12t-x (a) dx (b) dt…

A:

Q: S sin x (1+ cos x) ecos *dx 2. S csc ³ () do 1.

A: 1) Given:       ∫sinx1+cosxecosx dx Integrate by parts:         ∫fg′=fg-∫f′g here  f=1+cosx→f'=-sinx…

Q: use radians 2sinx + 1.5e^x + 1.25 Using Newton-Raphson method (upper limit) find the x intercept…

A:

Q: sin y dy dx If 1 for some a > 1, then the value of a is y 0 x

A:

Q: Original Sound ff EXERCISE dy -x = x2 siny dy 3 -(-siny ANSWER: X = %3D

A:

Q: Lv f(t) dt = In(x) cos(x) + Given f(t) dt, find f (x). You may find FTC 1 useful. sin(3)

A: 1(c).  Given that ∫sin(3)xf(t)dt=ln(x)cos(x)+∫e-t3f(t)dt To find: f(x)=?

Q: (f) ) (3x − 1)√√x² + 2xdx - (8) / sin". (h) [ sinh r cos adr sin x -dx √cos5 x

A:

Q: 75. Evaluate | (sin-x)? dx. Hint: Use Integration by Parts first and then substitution.

A:

Q: y = (sin-lx)sinx Q3) Find dy /dx for the following implicit functions : y?.sin(x.y) = tanx %3D

A:

Q: f (x) = xe-* – sin?x Newton Raphson (1st Method) @ x1 = 0.5 Newton Raphson (2nd Method)@ x1 = 0.5…

A: Newton Raphson Method:- Hence by Newton Raphson Method Root of the equation is 0.61447 (correct…

Q: 3 T lavi cos x + sin x %3D

A:

Q: 11. ſ sin? x cos² x dx

A: Given ∫sin2x cos2x dx

Q: Sovle the initial value problem described by PDE: u, - cu = xe' with the data и (х, 0) %3 sin x,…

A:

Q: Find the equation for a sine function with: 32 • Amplitude = 3 • Period = • Phase shift = (-) n •…

A:

Q: d 6. dx sine 1 sin(x²) (B) (D) – sint=") (A) – x sin(x²) (C) x sin(x²)

A:

Q: Find the general solution to the differential equation y + 9x³y = x² It is not possible to express…

A: The given differential equation is y'+9x8y=x9. Let I=∫ex9dx+C. Comparing the given differential…

Q: cos x II. S .dx V1-2 sin x III. Stan³x sec*x.dx

A:

Q: Integrating sin(x) dx by parts in correct way, we obtain an expression Of the form A-SB dx , then B=…

A:

Q: Z=sin(X) + cos(Y) X from 1 to 10 (increments of 0.5)

A: % Matlab script to create 2 subplots (mesh and surf) % create the matrices X, Y both between…

Q: The integrating factor that can be used to turn the following non-exact equation into an exact…

A:

Q: I) sin X dy dx Sin 2X - y Cos X

A: Explanation of the answer is as follows

Q: Let c be the number such that the area under y = sin x over [0, x] is divided in half by the line y…

A: Consider the provided question, The area under the y = sinx is find as by integration,

Q: 2T -TT Evaluate: S. (sin x + cos y)dx dy II SII 71I

A: Let give integral is equal to I

Q: The displacement x of a moving object at time t is given by the equation .2 X= cos tsin°t 3 The…

A:

Q: X is used to estimate the value of sin x at x = 0.3. 6 Estimate the error if P 3(x)=x- |Error| <…

A: P3(x)=x-x36 is used to estimate the value of sinx at x=0.3

Q: 1 (s +1)(s² + 1) - cos t + sint) + cost – sin t) Option 1 Option 4

A:

Q: L {t®e-%t} L{e-t cos 2t} L {2e3t sin 4t}

A:

Q: sin(x) d Find (S sin (4 t) dt). cos(2)

A: Use the concept of derivative of an Antiderivative.

Q: Use integration by parts to derive a reduction formula for x"e dx. Use the result from part 1 to…

A:

Q: 1. Find for, (x + y)* = tan-14x + T* dx InIny

A:

Q: 2T d) f(x)=5 sin (x+1)+2 e) f(x) = -2 cos 2(x+ 1) + 1_ 17. Find the rule of the sinusoi

A:

Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Given: h(y)=sin(y+1) At, y=0

Q: Integration by parts. cos?x – dx sin4x

A: Given:        ∫cos2xsin4xdx Rewrite/simplify using trigonometric/hyperbolic identities: we know that…

Q: (c) 1. f(t) dt = In(x) cos(x)+ sin(3) L e-" f(t) dt, find f(x). You may find FTC 1 useful. sin(3)…

A:

Q: find critical points? y=2(1-x2)1/2 +sin-1 x

A:

Q: G/ Integration Fuctions: Sco55 (3x) sin(³x) dx = - (08 (78) 18 A true B Error +C

A: To determine whether the given integral solution is correct or not.

Q: 2. Approximate (x-3) dx using 4 rectangles. It is approximatiley (If necessary, round to two decimal…

A:

Q: X Evaluate the integral [sincos dx. X sin cosdx= 5 C

A: The objective of the question is evaluate the indefinite integral.