If we use Trapezoidal rule to approximate * f(x)dx then find the value of x2, where n= 6 Select one: а. О O b. * 3 c. \( \frac{ \pi }{6} \) d. \( \frac{ \pi }{4} \)

Q: The TrapZoidalrule for fdx = 5 and Midpointrule %3D fex) olx = 4 what value does Simp Sans rule give…

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Q: Use Midpoint rule and Trapezoid rule as a pair to implement adaptive quadrature rule to approximate…

A: Mid Point Rule: The mid point rule approximates the midpoints of the sub intervals. i.e, ∫abf(x)dx…

Q: SOLVE USING VAREATION Of PARAMETERS OR REDUCTION of ORDER 2 tan'x

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Q: EX / Show that cosh x-sinhx=1

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Q: В. Estimate to three decimal places the value of: S V1 + x³ dx by using the trapezium rule with n =…

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Q: 8. Informally explain how the length of a curve defined by a function be computed with an integral.

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Q: Find a curve through the point ( 1 , 5/6 ) whose length on the interval [ 1 , 2 ] is given by ∫ 1^2…

A: The length of the curve y=f(x) from x=a to x=b is L=∫ab1+dydx2dx Now , Length of a curve on the…

Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

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Q: Find the root of the function using Fixed-point Iteration. f (x) - x cos (x) - x?

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

A: Given:        ∫02x2+1dx       n=4 , a=0, b=2   Midpoint Rule…

Q: By using the definition of hyperbolic functions, show that sinh x = 1 (cosh 2x – 1). -

A: Given,         sinh2x=12cosh2x-1

Q: tan(2r) lim 3r+ sin(x)

A: As we know that: limx→afxgx=limx→afxlimx→agx And we know that the identities of limit.…

Q: Find y' if y = 5x + 2 using the limit definition derivative

A: Y'  or 1st derivative is evaluated using limit.

Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

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Q: 2- Find the positive root of f(x) = xe"- cos(x) with an error tolerance =0.005% by using the secant…

A: Using a graph, it can be found out whether a function has solutions if the graph cuts the x-axis at…

Q: =[in(4-x cos (r4

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Q: Use the first derivative test to find and classify the relative extrema of x2 +8x+ 16 f(1) = For…

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Q: use the general power rule or the shifting and scaling rule to compute the derivative  Y= cos4(ϴ+6)

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Q: Apply the first derivative test to indentify all relative extrema. f(x) = cos² (2x)

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Q: (Use Simpson's Rule with n=4 to approximate 5x* dx

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Q: Use Simpson's Rule with n = 4 to approximate 5x* dx.

A: The solution is given as

Q: Use the trapezoidal rule with n = 5 to approximate cos(x) -dr Keep at least 2 decimal places…

A: The trapezoid rule is

Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

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Q: Find the derivative y using limit  definition y=6x^2 +4x

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Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

Q: What is the length of the arc y = (x6/6) + (1/16x4) on the interval [1,2]?

A: Given, function and interval

Q: FInd the length of the curve y= 2ln ( sin(x/2)) from x = π/5 to x = π

A: Formula to find the length of the curve is  ∫ab1+dydx2dxGiven y=2ln(sinx2) Lets find out dy/dx by…

Q: Find the root of the equation using any bracketing method: f(x) = x2 – sin x - 0.5 with an upper…

A: Bisection Method:This is one of the simplest and reliable iterative methods for the solution of…

Q: If tanh(x) = 24, find the values of the other hyperbolic functions at x. sinh(x) %3D cosh(x) coth(x)…

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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: How are the intervals similar where the graphs of y=sinx and y=cosx are increasing and where the…

A: The interval where y = sinx and y = cosx both increases is x =3π2±2nπ,2π±2nπThe interval where y =…

Q: 9. y = 3x – Vx

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Q: Q3: Find value of x if 3 cosh x- sinh x= 4

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Q: Find the length of the arc y = 8. 1 from X = 1 to x = 4. 4x www

A: Given

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Q: Find the equation of the tangent line at (3, f(3)) when f(3) 17 and f' (3) = 4. (Use symbolic…

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Q: Find the possible values of cosh x that satisfies sinh²x – 3 cosh x + 3 = 0

A: We use the following identity to solve question 1). cosh2x - sinh2x = 1

Q: If sinh(x) = 35 =, find the values of the other hyperbolic functions at x. %3D cosh(x) tanh(x)…

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Q: Use the trapezoidal rule with n = 8 to approximate cos(x) -dx Keep at least 2 decimal places…

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Q: Find limit   without using derivative

A: Given,

Q: Find sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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Q: Find the derivative by the limit process. F(x) = 13 -

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Q: Use the composite Simpson's rule with step length h=0.5 to determine 1= [ (2x - - 3x2 + 4x – 1)dx,

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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 length of the arc y =: 8 1 from X = 1 tox = 4. 4x?

A: Graph: Given: y=x48+14x2. So,          y'=x48+14x2' =x32-12x3.

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: