Determine L '{F}. s?F(s) s+5 + 3sF(s) – 10F(s) = %3D 2 s+ 6s

Q: Differentiate y = 2(2x - 1)5/4.(2x + 1)3/4

A:

Q: fx*V5-x°dx

A: In this question we will use basic of calculus i.e concept of integration. We will simply use the…

Q: Find f. 36x2, f(1) 15 f "(x) = 10 + 6x + f(0) 4, f(x)

A: Given,

Q: 1. f4x-³ dx -3

A: Find the integral

Q: +*- 2x+ 2y = ? d²y +x2 dx2 dx3 %3D

A: In the question it is asked to solve the differential equation shown below.

Q: ャX+4..dx x* + x²_ 2x の (2

A:

Q: S= 2rh + 2r^2 , for h Please show steps

A: Do the mathematical operations such that only h remains one side and other all shifted to others…

Q: Evaluate ∫4x+5/(3x+2)(x+3)dx

A: Given Integral: ∫4x+53x+2x+3dx   To find: Evaluate the given function. Formula used: i) Partial…

Q: Y/9-2/5=1/3 Show also the checking

A: Solve and check the equation Y9-25=13.

Q: Evaluate 4x² + x3 2x² – 3x - 2 dx.

A: the given integral is (4x2+x-3)/(2x2-3x-2).

Q: lim (Vx2 + x (v. – x

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Q: Find f. f"(x) = 6 + 6x + 36x², f(0) = 3, f(1) = 14

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Q: Differentiate and simplify. f(x)=Je* +In (x² +4)

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Q: 192) Find la(21)=?

A: Note the logarithm property : logaxy=logax+logay where x,y>0 and a>0 ,a≠0 . logaan=n ; where…

Q: x/2(2x + 7)* (3x² + 1)? Differentiate y = In

A:

Q: Evaluate d (2 – 1) (z + 7)] | da O 3x^2 + 14x + 1 3x^2 14x + 1 O 3x^2 - 14x - 1 3x^2 + 14x - 1

A:

Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Q: Draw y² = f(x) 1+ (1,-1) 2 (2.5,1)

A: We have draw the graph of y2=f(x)The procedure is given below

Q: 1 2 (2.) } ² dx 2 2 ²x + 4x + 5

A:

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.