Pure Mathematics Degree

Introduction to pure mathematics degree:

Pure Mathematics is planned for students with a strong mathematical environment and also helpful for higher graduate students.  The subject mathematics contains calculus, differential functions, unit measurements, number sense, groups, numerical methods, fractions & mixed numbers, vectors, algebra, geometry, algebra function, probability and statistics number using words decimals. In this article we shall discuss about pure mathematics degree. I like to share this Vector Calculus Identities with you all through my article.


Problem on differential function- Pure mathematics degree:


Example problem1:

To find `f` `^'(x)` the function of` f(x) = x^2+2x+3,` when `x=2.`

Solution:

`f(x) = x^2+2x+3`

`f^'(x)=2x+2`

`f^'(2) = 2(2)+2`

`f^'(2) = 4+2`

`f^'(2) =6`

Answer is` 6.`

Example problem2:

To find `f^'(x) ` the function of` f(x) = x^2+2x+3,` when `x=3.`

Solution:

`f(x) = x^2+2x+3`

`f^'(x)=2x+2`

`f^'(2) = 2(3)+2`

`f^'(2) = 6+2`

`f^'(2) =8`

Answer is `8.`

Example problem3:

To find` f^'(x)` the function of `f(x) = x^2+2x+` `3,` when `x=4.`

Solution:

`f(x) = x^2+2x+3`

`f^'(x)=2x+2`

`f^'(2) = 2(4)+2`

`f^'(2) = 8+2`

`f^'(2) =10`

Answer is `10.`

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Calculus problems-Pure mathematics degree:


problem 1:- Pure mathematics degree

Integrate the known expression with respect to `x: int 12x^4 - 11x^5 dx`

Solution:

Given` int 12x^4 - 11x^5 dx.`

Step 1:-

`int 12x^4- 11x^5 dx = int 12x^4 dx. - int 11x^5 dx.`

Step 2:-

`= int 12x^4dx. - 11 int x^5 dx.`

Step 3:-

`= (12x^5)/ (5) - (11x^6)/ (6) + c.`

Step 4:-

`int 12x^4 - 11x^5 dx = (12x^5)/ (5) - (11x^6)/ (6) + c.`

Answer:

`int 12x^4 - 11x^5 dx = (12x^5)/ (5) - (11x^6)/ (6) + c`

problem 2:- Pure mathematics degree

Integrate the known exponential function: ` int tan x + e^ (2x) dx`

Solution:

Step 1:-

`int tan x + e^ (2x) dx = int tan x dx + int (e^(2x)) dx`

`= int tan x dx + e^ (2x)/ (2)`

Step 2:-

`= - log (cos x) + e^ (2x)/ (2) + c`

Answer:

`- log (cos x) + e^ (2x)/ (2) + c`