2nx- Let f: R → R, f(x) = sin (). a) Solve the equation sin ()= - for x e [0,3]. 2nx.

Q: Determine fry when f (x, y) = x sin¬' () -1 1. fry = (x² – y?)3/2 y? x² – y? 2. fry - xy 3. fry (x²…

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Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: i) dt (1+t)3 j) S(sin?x cos x)dx x+3 k) S: -dx x2+6x-11

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Q: sin, ifx T 2л

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Q: Find f(x).

A: Given,

Q: (b) Let f(x) = sin (cos-1 (sin(cos-vx))).B f'(1) = using chain rule, show that %3D

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Q: V. Let z be a function of r and y, and tan y2 + x2 = z*ey. Solve for dz dz and

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Q: a) f(x) = 3x + 5; interval [1,2]; %3D W = 10 interval ; 11m- b) f(x) = sin x;` %3D W = -1 2' 2

A: To verify the IVT for the specified function f, the interval a, b, and the indicated value w.a…

Q: 17. Derive A) f(x) = 10x* –- 32x + e² %3D B) y = e-* sin x

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Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: f(t) = cos(t/2) - sin(t), in the interval of [-T,1].

A: The given problem is to find the Fourier series expansion of the given periodic function with given…

Q: For the function f(x,y)= (x² + y²) tan(ln(xy)) + e(x-y) which of the following is the value of…

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Q: #2. | Ax)dzx, f(x)= (sin z, 0srs a/2 |cosr, n/2< rSA f(x)dxr. f(x): #3.

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Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? A 1 B)…

A: Given that ∫x sinx cosx dx=fxsin2x-gxcos2x+C

Q: 4- f(t) = ,"t sin(t) e-S'dt

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Q: Integrate the function. 49-x dx 49x O A. + +C 2. 49-X 49-X +C B. 4949-x2 49 X49- x2 + C c. -1 sin +.…

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Q: d) f(x) – e) f(x) = sin [In (x² - 3x)] sin x f(x) = 1+COS X

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Q: sin(x³ + y* ) Q3. Find of for the functions: .(x.y) (0,0) x'+y f(x.y) = .(x.y) = (0,0)

A: f(x,y)=sin(x3+y2)x2+y2 uv'=vu'-uv'v2

Q: Given, f (x, y) = sin (x²y – 2x + 4). Find fy. - x cos (x²y – 2x + 4) x² cos (x²y – 2x + 4) O-x² cos…

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Q: a) f(x) = 1+ Sinx for all x e R

A: According to the question, we need to plot the graph of the function: f(x) = 1+sin x The graph of…

Q: Using FPI, find a critical point of the function: f(x) = x2 – 2e* cos x With an initial guess, xo…

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Q: Let f(x)= sin(x) – e¯*, po=0, and p,=1, then by Secant method p2=

A: f(x) = sin(x) -e-x  p0 = 0 and p1= 1

Q: dx -= In[F(x)]+C• What is F(/3) if C = 0? For J (x+x³) (x Tan-'x+1) + 6 + -1 +

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Q: Using the substitution t = tan(), the integral 2 dx sin(x) – 78 cos(x) can be written as dt 39 – t-…

A: To make substitution and re write the given Integral.

Q: Evaluate | f(x) dæ, where -T< x < 0 f(x) = 15 sin(x), 0< æ < n. | f(x) da = -T

A: Solve the following integral

Q: Let f(x) = – x^3 – cos(x), po= – 1, and p,= 0, then by Secant method p2=

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Q: 3. If f(x) = cos(x), determine f(125) (-T). V2 (B) 2 (A) 0 (С) 1 (D) –1 1 (E)

A: we will use nth derivative formula of cosx .

Q: Find the orginal function of this A Fx) =-1 (B) Frz)= X +1 ニー re Fez) s -x+3 tan x - sec3x

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Q: If f(x) = x sin x), then f' (x) = V1-x2 (B) sin-1(x) – x sin-2 (x) (C) + sin-1(x) 1-x2 (D) -…

A: Given that         f(x) = x sin-1(x) Here we have to find f'(x).

Q: a) f(x) = 1+ Sinx b) f(x) = x² + 2x- 1 c) f(x) = 2* + 2 for all x eR for all x eR for all x eR

A: Given function are: [1] f(x) = 1 + Sinx   for all x ∈R [2] f(x) = x2 + 2x - 1  for all x ∈R [3] f(x)…

Q: off f(x) dx, where Evaluate [ f(x) f(x) dx = f(x) = 18x², -T≤x≤0 19 sin(x), 0≤x≤T.

A: We have to solve given Questions.

Q: f(x) = /sin(e² cos(z) f' (x) =

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Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

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Q: 2s Prove that L(t sin t) (s²+1)²

A: We can use the concept of Laplace transform in order to solve the given problem.

Q: 1+ x² -L „tanx - for all x €[0,1/2], then f'(x) equals 1+ ex * If f(x) = sec2x A 1+ etanx sec³x B 1+…

A: Given an integral. We need to find f'(x).

Q: Q5) Find f((s) if you know that g(x) = cos(x² – 1). S(x) = 3tan(x*) at vr?

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? A 1/2 B…

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Q: y2 Use the modified Euler Method to solve the ODE = dx subject to y = 1 when x = 0 1+x on the…

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Q: 2. Find g'(x). -sin x g(x) = [? t²et dt %3D x3

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Q: y for the function f(x)= cos [x*sin (x²+1)] =, CoS 1/2 %3D ..…

A: The given function is fx=cos3x3sin12x2+1. Obtain the derivative as follows.

Q: The function f : XI→ a + b cos x, is defined for 0 sxs 2n. Given that f(0) = 10 and that f (n) = 1 ,…

A: The range of a function is the values that can be obtained from the function by substituting all the…

Q: ind the linear approximation of the function at the given point. x_ v) = -4 sinx+ 7 cos y at (0, 7…

A: Hey, Since you have posted multiple questions we will answer only first question.

Q: dx - is 2/x - Sin| x +s|+c. Vx +5 The antiderivativeof - A) True B False

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Q: Evaluate f(x) dx, where 8x', ={ 7 sin(x), 0<x< a. -T < x < 0 f(x) :

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Q: a) Find the linearization of the function f(x) = cos(x) at a = π/2, b) Use a) to approximate…

A: (a) We have,

Q: Let f(x) = 3 sin'x - 7 cos(2x), 0 <xS T. Find the interval(s) on which f is increasing. (A) (0, 7)…

A: Recall that, f is increasing on (a,b) if f'(x)&gt;0 in (a,b).

Q: Consider J x sinx cosx dx = f(x) sin2x-g(x) cos2x + C. What is the value of f(1) + g(1)? A) 1 B) 1/2…

A: We have to find the integral

Q: f(æ) = / t2 – 9 dt 1+ cos? (t) At what value of x does the local max of f(x) occur?

A: Given: For the local maximum value of f(x), we must have f'(x) = 0. Here,…

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.