Determine values of M that will ensure an approximation error of less than 0.0002 when approximating sinx dx and employing Composite - Simpson's Rule. (Hint: Use the error formula E (f ,h) -b-a) h+f(4)(c),a

Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = ex sin y at the origin. Estimate…

A: The given function is,

Q: 2 Use the trapezoidal rule with n = 5 to approximate sin(x) -dx. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,5…

A: Trapezoidal rule

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0. f(x) has a root in - [o]. If we use…

A:

Q: Find th epwation of the tangent line to An- (x-2y): 2xy-1 at print (1, 2) d [sin- (x-2g)] = (2xy-1)…

A:

Q: 6. Use the Successive Approximation method to find correct to four significant figures a real root…

A:

Q: The slope of the tangent line to the curve at the point where x = O +1 -1 DNE f(x) = sin² x cos²x

A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin.…

A:

Q: Use Newton's Method to find an approximation of V5+1 accurate to within 10-3

A:

Q: 14. S 5 sin 3x cos 3x dx 15. ſ tan? Ode

A: We can solve the given integral as follows:

Q: Find the maximum possible error in the computed value of the hyperbolic sine function, sinhx = at…

A: Solution

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)&lt;0 and f(b)&lt;0.…

Q: Use forward and backward difference approximations of O(h), and a centered difference approximation…

A: Given function is, fx=sinx1+cos Then the forward Oh is,…

Q: Use differentials (or equivalently, a linear approximation) to approximate sin(40°) as follows: Let…

A: Given, f(x)=y= sin 40° Therefore, f'(x)= y'= dy/dx= d(sin 40°)/dx f'(x)= cos 40°

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ (x) has a root in - [0]. If we…

A:

Q: The slope of the tangent line to the curve r=cos20 at 0= 1/4is none of these O-V3 0 1 O (-1)/V3

A: As we know that; The slope of the tangent line to the polar curve at the given point is equal to the…

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: Use Newton's method to approximate a root of the equation 3 sin(x) = x as follows. Let x1 1 be the…

A: The given equation is: 3sinx=x Let x1=1  be the initial approximation  To find the second…

Q: ÿ + ỷ = sec t tan t

A: This is the question of the differential equation.

Q: Find the slope of the tangent line to the sine function at the origin, (a) y = sin(4x) 15 y'(0) = 4…

A:

Q: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: 1. Estimate the root of the expression, f(x) = x² – cos x, using: c. Newton's Method using x, = -1…

A: The equation in form f(x)=0 is called a transcendental equation. The solution of the equation is…

Q: 10 Use Simpson's Rule with n = 8 to approximate f cosx dx. 2

A:

Q: Use Newton's method to approximate a root of the equation cos (x2 + 3) = x° as follows. Let x1 = 2…

A:

Q: Use Simpson's rule with n = 6 to approximate %3D cos(a) dx 0.08 Keep at least 2 decimal places…

A:

Q: 2. Find a root of f(x) = 6 Sin (x)e* + 1 using Newton Raphson Method accurate to 5 decimal places.

A:

Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: Use Newton’s method to approximate an intersection point between f(x) = tan(x) and g(x) = 2x. Use…

A:

Q: Use Newton's method with the specified initial approximation x1 to find x3, the third approximation…

A:

Q: use a geoetry formula to find the exact value of the definite interval (-2x+4) dx on the interval…

A: The given function is (–2x+4) with the interval [0,3].

Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in - [0]. If…

A:

Q: In estimating cos(4x)dx using Trapezoidal and Simpson's rule with n - 10, we can estimate the error…

A: a = -1 b = 6 n = 10   h = (b-a)/10 = 0.7 h = 0.7   f(x) = cos(4x)   f'(x) = -4sin(4x) 0 = -4sin(4x)…

Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27.…

A:

Q: .Find the estimate for the root of f(x) = sin x+ cos (r+1)-1using Bisection methodx, = 1.5, X=2 with…

A: Solution

Q: Find an equation of the tangent line to the graph of f(x) = | t cosh (t² – 1) dt tan-lt 1+In (x) at…

A:

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0, f(x) has a root in [0]. If we use…

A:

Q: 6. In(x*y?) %3D х* +уз 7. У- Arccos(e2x)

A: Given In(x3y2)=x2+y3y=cos-1(e2x)we need to find the second derivative of the given equation

Q: Find a root of the equation 3x + sin(x) - e* = 0 using Newton Raphson Method. Consider initial guess…

A:

Q: 5. Use the forward and backward difference approximations of 0(h), and a centered sin(x) difference…

A:

Q: Use Newton's method to solve for x with an initial estimate of x0 = 2n with d* < 0.001. Cosxcoshx =1…

A: (cos(x))(cosh(x))=1f(x)=(cos(x))(cosh(x))-1ddx((cos(x))(cosh(x))-1)=-sin(x)cosh(x)+cos(x)sinh(x)⇒f'(…

Q: The third derivative of y = sin(2.x) is (A) None of the given choices B y" = 8 cos(2æ) © y" = -8…

A: This question is related to differentiation, we will solve it using given information.

Q: For what r-value (approximately) does the function f(x) = sin(x) – 2? (Use x = 2 as a first…

A:

Q: 2. Use Newton's method to find the second approximation x2 to a root of the equation r + 3x – 1= 0,…

A:

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

A:

Q: Find the derivative of the function. y = 6 In sin 22x O A. 24 sin 2x OB. 12 In sin 2x C. 24 cot 2x O…

A: We can find the derivative on the given function by using the chain  rule of differentiation.

Q: Using Newton-Raphson Method, estimate the root (6 decimal places) of the following: f(x) = 3x-e cos…

A: The newton-Raphson formula for the roots is given by xi+1=xi+f(xi)f'(xi), where x is the root of the…

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: Find the actual error when the first derivative of f(x) = sin(2x) at *=1/8 s approximated by the…

A:

Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

A:

Q: 1. (a). Find the linear approximation to f(x) = sin x at = 0, (b). use it to approximate sin(-0.01).…

A: We have to find the linear approximation and percentage error.

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.