Q.5: Derive reduction formula of f cot"x dx. Also prove that -cot*x cot2x S cotx dx = + InSinx + C. 2 %3D 4

Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: тт Find the absolute minimum and maximum of f(x) = 2 sec x tan x on the interval [-- 4' 4

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Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

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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: 2. If f(x) = cos2x, find f(0), f(--).f),f(-x) 3. If f(x) = x(x+1), show that f(x+h)– f(x)= h(2x +1+…

A: 2. f(x) = cos2x , find f(0) , f(-π/4), f(7π/8) ,                                         f(-x). f(0)…

Q: what is the largest vertical distance between the graphs of the functions y=x^1/2 and y=x^2 in the…

A: To find the largest vertical distance between the graphs in the interval given

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

A: Solution

Q: 26. Show that the function has removable discontinuity at the origin sin 2x 2x f(x) = {Z 1 if x = 0…

A: Given f(0)=1 now we have find   limx→0f(x)=limx→0(sin2x2x)=1  ( By property)

Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

A:

Q: 2. A particle moves along the parabola y = x in the first quadrant in such a way that its…

A: Given: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x -…

Q: Find the absolute extremum point(s) of f(x) = e' -Cos x on [-골, T), E any.

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Q: . How many point(s) of inflection are on che graph of f(x)=18x^3+5x^2-12x-17 * f(x) = 18x + 5x² -…

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Q: * Graph f(x) = 3 sin (x) on the interval [0,4]. Be sure to laber maximum, minimum, and x intercepts.…

A:

Q: Determine the points in the interval (0, 2n) at which the graph of the function below has a…

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Q: a) Differentiate f(x) = sin x from first principtes. %3D

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Q: use graphical approximation methods to find the point(s) of intersction of f(x)=e^x and g(x)=x^6 to…

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Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, 1]?

A: follow next step

Q: What is the minimum value of f(0) in the equation f(0) = 3 sin 40? %3D

A: To determine the minimum value of the below function. fθ=3sin4θ

Q: Q1- Prove that coth x = 2 csch 2x + tanh x

A:

Q: Find all points on the graph of the function f(x) = 2 cos(x) + cos2(x) at which the tangent line is…

A: Horizontal tangent is parallel to x axis hence slope of tangent is zero at that point

Q: If f(x) =- 2-cos(x) sin(x) then the absolute minimum of f on the TI 3T is: interval O 2/2-1 O 2/2+1

A: Steps to find the absolute minimum value : Find the critical point of f Evaluate the function…

Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

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: Use Newton’s method to find the absolute maximum valueof the function f(x)  =x Cos x , 0 ≤x ≤…

A: The given function is

Q: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

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Q: Sketch the graph of two functions g(x) = cos x and h(x) = on the same plane. Choose [a, b] that…

A: Given g(x)=cosx and h(x)=x/2

Q: What is the largest vertical distance between the graphs of the functions y=√x and y=x 2 in the…

A:

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 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: Use Simpson's Rule with ne4 to estimate Cos"xdx COSTX ☺ For ☺ an upper bound for the estimate. Hint:…

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Q: the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in the form y =…

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Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

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Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: 1 Use the definition of the hyperbolic functions to prove the identity 1– - = tanh?(2x) cosh?(2x)

A: Explanation of the answer is as follows

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

A:

Q: At which points does f(x) = 2 sin x - cos 2x have an absolute maximum value and what is the maximum…

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Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -pai to x =…

A: given

Q: 13 Use the Linear Approximation to estimate Af for f(x): when a = 2 and Ax = 2+x %3D (Use decimal…

A:

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

A:

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1- - tanh? (2x) cosh (2x)

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Q: 1. Find the point(s) if any where f has a horizontal tangent line. у %3D УЗх + 2 cos x 0<x < 2п

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Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, n]?

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Q: (i) By making the substitution o = tan 0, demonstrate the validity of %3D Parseval's theorem for…

A: Consider the function as ft=e-tdt

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: Suppose that a particluar funciton f satisfies f" (x) = - (4 sin(x) + cos(x)), f(0) = 3, f'(0) = 5.…

A: f"(x) = -(4sinx +cosx) ,  f(0) = 3 , f'(0) =5 now integrate the f"(x) f'(x) =4cosx -4sinx +c now…

Q: Determine the maximum/minimum point(s) for y=sin 2x– cos x – 4x on the interval 0 <x< 2n . The…

A:

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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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.