What is (fo g)(11) if f(x) = V – 3 and g(x) = x – 7?

Q: If Fx) is an antiderivative of x2 +x1, then what is the value of F(1) - F(-1)? 3

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Q: x2y/5z x3 y4/10z3x4y5/15z4

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Q: A store is deciding what types of fruit to stock nearest to the registers. They can either stock…

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Q: If f(x) = Jx-3 then f(-3) + f(12) is

A: We can make it easier for you

Q: What is the value of f(1) - 16B in ∫x^3 lnx dx= f(x) ( (1/4) lnx - B ) + C

A: To find out the required value.

Q: f:R - R S6 – x2 x 2 1 x < 1 fx 4x + 1 x=1, x= -1-

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Q: #20

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Q: What is the value of f(1)-168 in [x³ Inx dx = f(x) ((1/4) Inx-B) + C? A) 2 B) 1 (C) D) 3

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Q: determine L−1[F].

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Q: (b) Let f(x)=√x and g(x) = 2x+5, find: (1)fog(x) (2)gof(x)

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Q: b) y =1+ f(z)=2x-2 O 1ks f-(z)=-1 O 2 34s (2)=2x-1

A: Step 1 Replace y with x and x with y  Step 2 Then solve for y in this equation  Step 3 Replace y…

Q: 3 11. f(x) = Vx-6Vx 12. f(t) = t3 -t3 +4 ww-

A: Basic derivative formula can be used to solve the questions. ddx(xn)=nxn-1ddx(cosx)=-sinx

Q: Find d²y/dx² for the following equatio: f) x2/3 + y2/3 = 1 g) x³ + y4 = 16

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Q: x²–1 If f(x) and g(x) = Vx – 1, which will yield (f 0 g)(x)? %3D r2

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Q: c) f(x) = 2* + 2 for all x e R

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Q: (c) f(x) = x4 - 1 and g(x) = x4 – x³ – 3x² + 5x – 2 in F(R) -

A: HEre we have to find the GCD of the given polynomIal.

Q: What is the value of f(1) - 16B in 1 x³ Inx dx = f(x) ( (1/4) Inx - B) + C? 0 2

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Q: If f(z) = 5.7x +6.9, then, f(x+h) is:

A: Given : fx =  5.7x+6.9

Q: -x-1 a) y' = +2yi-1 v(0)=1

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Q: 8. f(x) = 2x +9x + 4 x² -16 a) HA at b) VA at (2x+1)(x+4) (x+4)(x-4)

A: From the given function: fx=2x+1x+4x+4x-4 As we know that for vertical asymptotes , equate…

Q: 2. 1. f (x) = x° – 4x – 5 g(x)3Dx5 a) Find(-)æ x + 5

A: Consider the functions

Q: b) f(x) = V3 + x² at x = -1

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Q: 2 f(x) = √4-x² [-1,1] n = 4 a = -1 right left & middle hand rule b=

A: The given function is fx=4-x2 over the interval -1, 1. The number of subintervals is n=4.

Q: For f(x, y) = 2x3 + x²y2 - 5y3 + 10,

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Q: (z+ 1)호(22-2z +3)호 (a2 – 4x + 8) When f(x) = find f'(1). %3D - (2전)

A: Given,         fx=x+112x2-2x+332x2-4x+812

Q: f (z) 10x +3 (2)) g (x) = -7x- 4 %3D What does (f-g) (r) e

A: To solve this question, We will use - (f-g)(x) = f(x)-g(x).

Q: 2 Given that f(x) = 4x – 7 and g(x) = 4 – a?, calculate (a) f(g(0))=| (b) g(f(0))=|

A: Answer(a): The given functions are: fx=4x-7 and gx=4-x2. Then, the composition function is given as:…

Q: (-x² +3, 3. f(x)={ Vx-3+1, x>2 %23

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Q: With f(z) = 5z² – 7z – 2, find the following: a) f(2) b) f(1) + f(0) c) f(r+h) – f(r - h)

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Q: How do I find the possible inflection points of f(x)=a/((x^2)+(b^2))? It also states a and b are…

A: To find point of inflection we need to find x from f"(x)=0

Q: The antiderivative of the function f(x) 6 + 8x is -8 + 3.0x2 + 6 + 4.0x2 + c 6 + 16.0x? + c -6 4.0x?…

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Q: 5x -1 7. f(x) = 3. a) HA at b) VA at

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: b) f(x, y)=-2x². + 8x − 3y² + 24y + 7

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Q: f(z) = x2 – 8x + 15 g(x) = 1 – 3 ()e) Find |(x) (1) The domain of

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Q: 1.3 Verify that f d = xp= x2V1+ x2 V1+ x² +c using the method you were taught in this course.

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Q: The Range of y = [2x + 1] is Z. FO * 2.2 2х-1 If y = Vx? – x then y' 3. 3 Vx2-x F O

A: Given(1)-      y=[2x+1]As we know that is set of all valid output values or all valid y values…

Q: (e) x = 4 – z2 - (f) x² – y² + 4y + z² + 2z = 0

A: x=4-z2 is a paraboloid and its graph is as follows

Q: What is the value of f(1) - 168 in [x³ Inx dx = f(x) ((1/4) Inx-B) + C? 0 1 3 2

A: Let's evaluate given integration.

Q: Find the value of x and y for f(x)=3x2+9xy-y2-9x,if fx(x,y)=0 and fy(x,y)=0

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Q: What is the value of f(1) - 16B in I x³ Inx dx = f(x) ( (1/4) Inx - B) + C? 2 0

A: Given; ∫x3lnxdx=fx14lnx-B+C    ...(1)   First, we have to find the integral value. I=∫x3lnxdx Apply…

Q: = x, find (f o g-3). Given that f(x)=2x+3 and g(x) (fo gX-3)-

A: (fog)(-3)=f(g(-3))

Q: -2 The domain of f(x,y) = is %3D x² + y?

A: f(x,y)=-2x2+y2

Q: Find Vf if f = 2 2 2 x² + y² + z² V.

A: Given,            f=1x2+y2+z2To find : ∇f

Q: Determine {F}. F(s) = 7s² - 13s +2 s(S-1)(s-6)

A: Let 7s2-13s+2s(s-1)(s-6)=As+Bs-1+cs-6       ⇒7s2-13s+2=A(s2-7s+6)+B(s2-6s)+C(s2-s)       ⇒A+B+C=7…

Q: Determine the value of ∫k4 f(x) dx given that ∫49 f(x) dx=−9 and ∫9k f(x) dx=−3.

A: We have to find following definte integral .Information is given below:

Q: b) f(x) = v3+ x² at x = -1

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Q: What is the value of f(1)- 168 in fx³ Inx dx = f(x) ((1/4) Inx-B) + C? A) 3 B 0 1 2

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Q: If f(x) = 4 – x² & g(x) = vx then find (fog)(x) » (gof)( x + 8 If f(x) = 3x – 8 & g(x) = then find…

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Q: How can we show that  f(t)=e4t-3t^2 is not an mgf?

A: For any Random Variable,  Var(X) &gt; 0 Now We know, E(Xr) = f(r)(t) |t=0 Where f(r)(t) denotes r th…

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.