Prove the identity. sec (-x) - sin (-x) tan(-x) = cosx

Q: 3 X is used to estimate the value of sin x at x = 0.3. Estimate the error if P3(x)= x -

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Q: Find  (f −1)'(a). f(x) = 3x3 + 3 sin x + 3 cos x,    a = 3

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Q: Number 33

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Q: 3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...

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Q: For (cos(2x) – sin cos(x) – sin(x) - sin(2x) cos (2x)) +C. What is F (x)? A sin cos³ (x) – cos(x)…

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Q: Evaluate cos x+ 2 cos x+1 dx sin x sin x - 3 cos x cost x 7. +x+c 2 cos x +x+c 3 cos X- cos x (sin x…

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Q: 5. tan (x)dx 1 -dx cos² (x) sin () 6.

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Q: cos²x 6. 1+ sin x = 1- sinx tanx - сotx 7. sec'x - csc?x = sin xcosx 8.1 tin cos2x = cscx - secx…

A: We have to verify that the given trigonometric identity.

Q: Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7]

A: Given y = 4 cos(x) - x

Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

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Q: 1 Find the mean value over the interval [0,2n]. 4+cosx

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Q: 1. S Vcos 20 sin 20 d0 x²-x 2. S- dp- (x+1)

A: To  evaluate the integral.

Q: The derivative of cos (x²) Graph y = -2x sin (x²) for –2 < x < 3. Then, on the same screen, graph…

A: We draw the graph of y=-2x*sin(x^2) using graphing calculator

Q: nd the mean value of sin 2x over the in

A: Here we have to find the mean value of sin 2x over the interval (0,x)

Q: 2 sin(x) cos(x) + v2 cos(x) = 0 COS

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Q: Find the critical numbers of the function. H(x) = sin^2x + cos x 0 < x < 2pi

A: For Critical points, put first Derivative of function equal to 0

Q: 75. sin x cos x dx 76. sin 2x sin (cos 2x) dx

A: as per the company guidelines, I can solve only one question.

Q: This problem requires integration by parts. Find ∫(xsinx)dx sin x - x cos x   - x cos x   cos x - x…

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Q: sin xV1+ cos 2xdx 6. V1 - sin 2xdx 7. 8. cos' xdx 1+x+x? -dx x² + x3 9. I sin 2x 10. I + sin² x xp-

A: Note: As per company policy we are supposed to solve only one question, So kindly repost the other…

Q: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: (2) Compute the value |* sin(2r)dr and show the computations involved. If you are using substitu-…

A: We use integration by parts.

Q: Find the absolute extreme values for f(x) - cosx - sin^2 x on the interval [-pi/2, pi/2] and…

A: Given:       f(x)=−cosx−sin2x;     −π2, π2

Q: Find Critical Points and Extreme Values: f(θ) = 2 Sinθ + Cosθ        on [ -2π, 2π ]

A: Given         The critical point is where  f'θ=0              Here the interval is -2π,2π…

Q: Proof 2: 14 sin x dx tan xdx = /6 COs x 1 -= sec x dv = sin xdx cos x du = sec x tan xdx v =-cos x…

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Q: 1-T= 3- Z= +cos(y)tan ( √x-b cos (n) 2-sin²(n) 2-B=sin(x) sec(x)/cscf(x) 4-(w+n)²(a+) x-3

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Q: ph of y = cos x from x = 0 to x = 27 by making a table using multiples of #/2 for x. y= cos x 2 EIN

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Q: 3x2 sin(x³) Select one: а. In/tan x3 + cot x³| + c b. -In csc x3 + cot x³| +c С. с. In|sec x3 +tan…

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Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

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Q: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

Q: The first derivative of the function h is given by h' (x) = 3 ln(2 + cos(2x)) x, and the second -6…

A: Given: h'(x)=3 ln2+cos2x-xh''(x)=-6sin2x2+cos2x-1-2&lt;x&lt;2

Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: Find the instantaneous rate: 1. f(x)=x²+9x+12; x=3

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

Q: (x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

Q: 1. sin x sin 2x + cos x cos 2x = COS X

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Q: 25 [x' sin xdx 27 |x' sin xdx 29 x’ sin xdx

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Q: cos" x dx Cosn-1 x sin x n – 1 + п-2 Cos' x dx n n

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Q: 6. Approximate the real root of x – cosx = 0 to three decimal places. Let xo = 0.8 and find x1, x2,…

A: Let f(x) = x - cos(x) x0 = 0.8 By using the Newton-Raphson method to approximate the root,…

Q: 6 x° cos(x) dx =. 6 x³ sin(x) + 18 x² cos(x) – 36 x sin(x) + 36 6 x³ sin(x) – 18 x² cos(x) – 36 x…

A: Integration by parts  ∫udv=uv-∫v.du

Q: Compare the accuracies of the approximations sin x = x and sin x = 6x/(6 + x2) by comparing the…

A: Given: The approximations . The functions and

Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

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

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Q: Find the linear approximation of f(x)=sin(x) at x=3π4 and use it to approximate sin(134∘). Give…

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Q: 2 sin'x - cos x sin'x - (1 - sin'x) in*s) Rule ? %3D sin°x - 1 + sin´x Rule ? %3D = 2 sinx - 1 Rule…

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Q: ∫ sin3 (x / 2) cos (x / 4) dx

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Q: 4 sin x cos x + 2 sin x - 2 cos x - 1 = 0

A: first factorize the given equation and than split two product equation  detailed solution is given…

Q: 1+sin x+cosx 1+cos x (b) 1+sinx-cos X sin x

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Q: Scos“ x- sin' xdx x•sin³ xdx 3

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Q: 2x² sin (x²)dx = V(1-x*) Select one: a. - sin-(x²) cos(sin(x²)) + x² + C b. - cot-(x?) sec(sin-(x²))…

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

A: Given function is, f(x) = 10 cos x + 5 sin 2 x The function has its horizontal tangent when its…

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.