sketch f(x)=sec x over the half-open interval -r,27). 2 1 3/% 27t 52

Q: Find an interval of definition for the equation x^2 dx/dt = 3x^3 t^2

A: Domain of definition is where X(t) is defined

Q: Q5. Use variation of parameters to solve the nonhomogeneous ODE. y" + 16y = sec³4x

A:

Q: 1) Given f(x, y) = x derivative of f? which of the following is Əyox the mixed second order par f

A:

Q: Integrate the following function by using trapezoidal rule. 142*dx

A:

Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

A:

Q: What is the approximate derivative of f(x) = x²ex, using backward-difference approach at x=2 and a…

A: The formula for the backward difference is f'x=fxi+1-fxih Now, h=0.1xi=2xi+1=xi+h=2+0.1=2.1fx=x2ex

Q: Let f '(x) = sinx - cos x. Where does the relative extremum value of occur? (a). 플 (b). (d). 프 (c).

A:

Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

A:

Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: The function f(x) = 1 + x decreases to 1 as x- 0. Does f(x) dx exist?

A: Given function is f(x)=1+x-1f(x)=1+1x Given integral is evaluated as follows.…

Q: Find the value of dy/dx at the point (-2, 1) for the function which is defined implicitly by x²y – -…

A: Differentiate wrt x

Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

A:

Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

A:

Q: Suppose f(x) = | sin(t?) dt. Find f'(x). x2

A:

Q: nd the points at which f(x) = cos² x has a horizontal tangent line. %3D

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Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

A:

Q: B. Use the trapezium rule with 6 ordinates to estimate fe* dx correct to two decimal places.

A:

Q: fro(x- dt show that = f(x). dx y 3

A: y=12∫0xft x-t2 dt

Q: Find the partial derivative. z = sin(4a'y – 5xy?) - az Əx

A: This question is based on partial derivatives.

Q: tan-lt t +0 t f(t) = 1 t = 0.

A: Given that, f(t)=1 when t=0. Differentiate the function with respect tot t implies, f'(t)=0  when…

Q: Evaluate the function: S de x(x-2) -dx (x–1)³

A:

Q: 1+e* dx diverges 0.

A:

Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

A:

Q: of of For the function f(x,y) = 4x* - 3y' - 8, find and dx of %3D dx of

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Q: Use the Quotient Rule to show that the Powers of x Rule appies to negative Integer powers. That s,…

A: The given function is fx=1xk   where k>0. Quotient rule says that ddxfg=gdfdx-fdgdxg2.

Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: The pdf of a continuous RV X is given by f(x) = cos(Ax)+ 10, where x E [0, -1. Find the value 2A of…

A: Given density function of the random variable X is, f(x)=cos(Ax)+10, x∈0,π2A The value of A is…

Q: Find the relative extrema (if any) of the function f(x) = sin 2x ; over the interval (0, π).

A:

Q: The finite difference approximation of the first derivative in the simple implicit method used to…

A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

Q: In the interval 3 < x < 4 of the first derivative test, f(x) is a. Not moving b. Changes direction…

A:

Q: Find the derivative(dy/dx) of following function f(x) = Sin(2x) (x+1)? %3D

A: It is derivative problem.

Q: The derivative of the function y = sin VE at a = is equal to %3D 4 14

A:

Q: (f) y = e* In(tanh(x))

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Q: The function f has a continuous derivative. If f (0) = 1, f (2) = 5, and f (x) dz 7, what is %3D %3D…

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Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

A:

Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

A: The given curve is- f(x)=lnsec(x)Interval 0≤x≤π4We need to determine the length of the given…

Q: Use the Trapezoidal Rule with n = 4 to approximate the value of: +1)dx.

A: Given,  ∫12x3+1dx, n=4

Q: dy Find for the following function: dx 1- y = etan'x

A: It is differentiation using chain rule.

Q: With n > 0, does x" dx get larger or smaller as n increases? Explain graphically.

A: Given: The given integral is ∫01xndx. Calculation: Use the integral formula, ∫xndx=xn+1n+1+C.…

Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: Find for the following function: dx 4- y = In2 5- tan-1 V4x - 5

A: Topic : differentiation

Q: Use the Trapezoidal Rule with n = 4 to estimate f, x² dx. Compare the estimate with the exact value.

A:

Q: (x+6)dx (x+2)?

A: To evaluate: ∫x+6(x+2)2dx

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;

Q: Find the length of the curve y = ln x from x = 1 to x = e.

A: Given:Find the length of the curve y = ln x from x = 1 to x = e.

Q: Find the slope of the graph of cos(x + y) = 2x at the point ( 0, T1/2 ). Hint: Differentiate…

A: