The range of the trigonometric function f(x) = sin (x - 5 is aY-0o, +0) b) [-1,1] c) [0,2] d) (–1,1) إختر أحد الخيارات (c) (d) (b) (a) o o o

Q: ind the slope of the tangent line to the curve 4 sin(x) + 5 cos(y) − 5sin(x)cos(y) + x = 3π at the…

A: To find the slope of the tangent line of 4sin x+5cos y-5sin xcos y+x=3π, differentiate it and…

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A: We know, ln(x) is defined for x&gt;0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

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A: Here the question is solving by using u-subsitution method.

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A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: sin x tan x 1.) lim 2.) lim 2x X-0 sin 2 x 1- Cos (2x) 3. lim X0 sin3x 4. lim x2

A: a)limx→0sinx2xSince on putting x = 0 , it is becoming 0/0 formSo, we'll solve this using…

Q: Prove that: 1) csc 0 + tan 0 . sec 0 csc 0.sce20 1-cos" x 2) sin x .cos x tan x 3) 3 cos' x-sia x+1…

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Q: Where are the theta valuss for the horizontal and vertical tangent lines on [0,2pi) of r=1+cos theta

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Q: In the interval [0, pi], find the absolute extrema of: g(x) = ex sin x - sin x + cos x

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Q: What is special about the functions f(x) = sin x - 1 x + 1' x 2 0, and g(x) = 2 tan Vĩ? -1 Explain.

A: Given that functions are f(x)=sin-1x-1x+1, x≥0 and g(x)=2tan-1(x). The graph of the function…

Q: sin-cos dt

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Q: Q.3) Prove that L-1 (coshat sinat + sinhat cosat) 1+4a4 2а

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Q: a Exercise: If L{sin (ax)} = p2+a2 then find L{x sin (ax)}. %3D Exercise: If L{cos(ax)} = p2+a2 then…

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A: Given:                      f(x)=sinxex on 0,π                     f(x)=e-xsinx     The mean value…

Q: 2. Using trigonometric substitution, what is f- vx²-9 dx ?

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Q: snip

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Q: a. Show that y = tan u increases on every open interval in its domain. b. If the conclusion in part…

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Q: Find the limit of the trigonometric function.

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Q: Sketch the midline and the graph of the function f(x) = 3 – 2 sin (플(-1) %3D

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Q: Prove that 1+ sin 0 tan 0 cos 0 + cot 0. Prove that (tan 0 + cot 0)2 1 sin² 0 ' sec2 0 + =

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Q: (폭), Let f (x) = x5 sin- Then %3D f'(x) =

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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…

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Q: Verify that the function satisfies the three hypotheses of Roll’s Theorem on the given interval.…

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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.