Which of the following is represents an estimate of L sin(x) dx using rectangles with heights determined by left-hand endpoints and four subintervals (i.e. n = = 4)? Select one: 4 Lo sin(x) dx z (1)(sin (0)) + (1)(sin (1)) + (1)(sin (2)) + (1)(sin (3)) 4 L sin(x) dx - (0.5)( sin (0.5) + sin (1) + sin (1.5) + sin (2) ) 4 L sin(x) dx x (1)(sin (1)) + (1)(sin (2)) + (1)(sin (3)) + (1)(sin (4)) L sin(x) dx z (1)(sin (1)) + (2)(sin (1)) + (3)(sin (1)) + (4)(sin (1))

Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: Preview and where B is: Preview

A:

Q: The linear approximation at x 0 to sin(2x) is A + Bx

A:

Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

A:

Q: Evaluate the following 1, the integral from 0 to π/2 of Cosx/(1+sin^2 x) dx 2, the integral from…

A: 1). the integral from 0 to π/2 of Cosx/(1+sin^2 x) dx   = arctan(sin(x))    Answer: π/4

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: Find dy/dx for y = (cos x) 2 + sin(x 2 )

A: Given that      y = (cos x)2 + sin(x2) We have to find dy/dx .

Q: Use Secant method with p, =1, p =1.2 to find the root of f(x)= ln x – cos x that is accurate to…

A: Solution:Let f(x)=log(x)-cos(x)a=1, b=1.2, f(a)=-0.5403, f(b)=-0.2832Here f(a)<0 and f(b)<0.…

Q: 11. Determine the values of n and h required to approximate e2r sin 3x dx to within 10-4. Use a.…

A: I am attaching image so that you understand each and every step.

Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

A:

Q: 68) Find a value of c that will make sin2 4x 0 x2 f(x) = C, x 0 continuous atx = 0.

A: Given,

Q: 3. Find a result by using exact for a. cos(x + y) dx + (3y2 + 2y + cos(x + y))dy = 0 2)dx

A:

Q: Find the slope of the tangent line to the curve: 3.) Ħan0 at 0=n/4 4.) sin20 at 0=x/3 5.) rcos20 at…

A: Use the formula for the slope in case of polar coordinate.

Q: 2. Evaluate the integral: | sinh x cosh² x dx

A:

Q: Only one of these calculations is correct to evaluate the definite integral V sinx dx Using the…

A:

Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: Steb by step

A: We will need integration by parts for this problem. So we assume u and dv and from there find du and…

Q: Find the extreme values for f(x) = sin(x) + cos(x) on the interval [0, 2π].

A: The given function is f(x)=sinx+cosx   and the interval is 0, 2π. We have to find extrema on the…

Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

A:

Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

A:

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: A-Evaluat wing integrais: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x=2. 3)…

A:

Q: The area under the entire curve is given by 00 dx. We have 3x-3 dx = lim 3x-3 dx -2 3x lim %3D -2 x…

A: the area under the  entire curve is given by ∫1∞3x3dx

Q: The approximation of 1 = cos(x+10) dx using composite Simpson's rule with n-3 is: 1.01259 3.25498

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: 1. Find dy for the following functions : dx Vsin x.cos x 1+2.ln x 3y (ans.: coi x 2 tan x -)) x(1+2…

A: To solve given differentiation easily we take logarithm on both sides and then differentiate it.

Q: Compute for the arcsinx dx . Which of the following is not an antiderivative of the function f(0) =…

A:

Q: Determine dy/dx given that: y = sinx - sin³ x O cos³x O cos x sin² x O sin³ x O - cos³ x -

A:

Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places…

A:

Q: Q1:Choose theappropriate value to integrate the following sin(In x) dx (sin (In x) – scos (In x)) +…

A: Solution I=∫sinin x dx        Let  lnx=t⇒x=et         1x dx=dt          dx=xdt…

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: 4. The given equation sinh(xyz) = x+ y + 3z implicitly defines a differen- dz Find ax tiable z as a…

A: Differentiate of sinh(x) =cosh(x)

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

A:

Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

A:

Q: 1. Prove: a. S csch x = In b. sech x = 2 Arctan(e*) +c ex+1 2. 2e* tanh e* dx 3. S sinh(5x - 1) dx

A: Given : ∫2extanhexdx Let us consider that : ex=u. Therefore, exdx=du. So, ∫2extanhexdx=2∫tanhu.du .…

Q: Find the indicated midpoint rule approximation to the following integral. .3 2 sin 7x 2 x dx using n…

A: Calculate the delta x and the f(xi) for the given integral.

Q: The approximation of the integral f(x-1) cos(x+2) dx using two points Gaussian quadrature formula…

A:

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

A:

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

A: Given integral is ∫0πsinxxdx. We have to evaluate the given integral by using composite trapezoidal…

Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: Find dy/dx for the following : 1) y = x + sin x² + stn-! 5x 2) y = 32x + In (stn x²) + In(sin-1 5x)…

A:

Q: The actual error of the approximation of I = x² sin (x³) dx using composite Simpson's rule with n=4…

A:

Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

Q: y=sin-1x

A:

Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

A:

Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: 4. Use Secant method with p =1, p =1.2 to find the root of f(x)= Inx – cosx that is accurate to…

A: Given, fx=ln x-cos x; p0=1; p1=1.2; As it is known that the secant method is given as,…

Q: 12) a) Use either the Trapezoid OR Midpoint Rule to estimate [ In(1+e* ) dx using at least four…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

A: