The inequality sec x > 1 + (x²/2) holds on (–7/2, 7/2). Use it to find a lower bound for the value of sec x dx.

Q: Using the forward difference and values of h=0.1, to approximate the derivative of cos(x) at…

A: This is a problem of Numerical Analysis.

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the Absolute Extremum of F(x)=2sinx-cos2x over [0,2pi]

A: Consider the following:  Differentiate the function and find critical point:…

Q: On the graph of f(x)=tanx and the interval [0,2π), for what value of x does the graph meet the…

A: x 0 π4 3π4 π2 π 5π4 3π2 7π4     tanx 0 1 3 ∞ 0 -1 -∞ -3

Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: Determine whether it converges or diverges. You must provide justification for your answer. |…

A: Answer is yes its convergent .

Q: Find the mean value of sin 2x over the interval (0,x)

A: Solution is given below:

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given function is fx=9-x2+sin-1x3.

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

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Q: Find f'a) for f(x)= =Sinx 1- Cos X %3D

A: We have to find the derivative of the given function.

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: • Use the trapezoidal rule with n = 14 to estimate: -dx √√1+x²

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Q: Use the inequality sin x 0, to find an upper bound for the value of sin x dx.

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Q: 1. Use the trapezoidal rule with eight intervals to evaluate places. I = [dx 3 2 %3D correct to 3…

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Q: ) Use Taylor's formula to estimate the error in the approximation In(x) ~ P3(x) or all x in the…

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

Q: State the Mean Value Theorem. Use it to show that for all x ≥ 0, 0 ≤ tan^−1 x ≤ x. [Hint: Use Dx…

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Q: Verify the formulas by differentiation. ∫1/(x + 1)2 dx = -1/x + 1 + C

A: Here f(x)=1x+12we have to verify that ∫1x+12 dx=-1x+1+C∫f(x) dx=∫1x+12 dxsubstitute…

Q: By using Trapezoidal rule, the value of “h" in evaluating (x² – 2x + 6)dx , by taking 10…

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Q: Use forward-difference formula to evaluate the first derivative of y = tan(r) at a = using a value…

A: We know that the forward difference formula is: f'(x)=f(x+h)-f(x)hThe given function is : y=tan(x)We…

Q: The approximation of the root x* of the function ƒ(x) = x* – 5x³ + 9x + 3 in the interval…

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Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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Q: Find and locate the local and absolute extreme values of f(x) = x+(sin2x) in [0, π].

A: Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].

Q: Find the absolute extrema of the function on the closed interval.

A: The given function is y=tanπx8    on  0, 2. Compute the critical points as follows.…

Q: Differentiate the following finction f(x)=sin(3 ln(x))

A: Given that the function is       f(x) = sin(3 ln(x)) We have to differentiate the the function f(x).

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: What values of a and b maximize the value of (x – x²) dx? |(Hint: Where is the integrand positive?)

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Q: Evaluate 0, dx by dividing the interval into 10 equal parts 8х-5 by using Simpson's one - third…

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Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: Which formula gives the x-coordinates of the maximum values for y = cos(x)?

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Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

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

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Q: The derivative of f(x) = ln( is cos x - Select one: O f'(x) = sinx O None of the other options O…

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Q: Use the Intermediate Value Theorem to show that f(x) = 2+ sin r 3 tan x has a | (0. ). solution in…

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Q: Estimate the value of df/dx for f(x) = root 8x at x = 3, using any method

A: To find the derivative of f(X), differentiate with respect to X on each side.

Q: 5 f(x) %D sin x

A: Given  f(x) = 5sin x We have to check the continuity of the function on the interval [0, 2π].

Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

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Q: II) By using the limit definition of derivative, prove the identity J dzf(2)8' (2) = - / da f…

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Q: Find a limit equal to (x2 – 8)dx. 3

A: The integral of some functions are given below. 1)∫x2dx=x33+c2)∫8dx=8x+c Use the above and find the…

Q: 1 3 + e2 + dx 2 (3х)3 2х2

A: The integral is ∫13x3-32x2+e2+x2dx. Evaluate the integral using u-substitution as follows.…

Q: Find a value of c that makes Continuous extension the function 9x - 3 sin 3x 5x f(x) = c, continuous…

A: The given function is

Q: a. Find the root mean square value of tanh x, for 0 < x< 2.

A: we know the formula of root mean square, rms = [ (1/b-a) (integration of |f(x)|2 from a to b) ](1/2)…

Q: How many periods of the function y = sec x are there between = and 3T -

A: Given: So, from the figure, it can be observed that only one period of y=sec x is there between -π2…

Q: Compare the Trapezoidal rule and Simpson's rule approximations to x sin x dx and find a bound for…

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Q: Find the interval in which function f(x) =sin (logex)+cos(logex) is decreasing

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Q: The vertical distance covered by a rocket from t 5 to t 30 is given by %3D 30 150000 2000 In 2100r -…

A: Given :-  The vertical distance covered by a rocket from t=5 to t=30s is given by  x = ∫5302000…

Q: a) f sin(x) cos(x) dx,

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

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Q: Solve f(x) Sin e* (12 intervals) Using Trapezoidal Rule(Numerical Methods) ['re f(x) dx

A: Solve the following

Q: dx by taking four 1+x Use Simpson's Rule to obtain the approximate value of intervals.

A: Given: ∫0111+x2dx Definition: If f(x) is continuous on [a, b] then Where, ∆x=b-an

Q: The graph of f(x) = cos x and a tangent line to f through the origin are shown. Find the coordinates…

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