HSC Commerce: Marketing and Salesmanship इयत्ता १२ वी - Maharashtra State Board Important Questions

Complete the following activity to find MPC, MPS, APC and APS, if the expenditure E_c of a person with income I is given as:

E_c = (0.0003)I² + (0.075)I²

when I = 1000

Slope of the tangent to the curve y = 6 – x² at (2, 2) is ______.

Find the value of x for which the function f(x)= 2x³ – 9x² + 12x + 2 is decreasing.

Given f(x) = 2x³ – 9x² + 12x + 2

∴ f'(x) = `squarex^2 - square + square`

∴ f'(x) = `6(x - 1)(square)`

Now f'(x) < 0

∴ 6(x – 1)(x – 2) < 0

Since ab < 0 ⇔a < 0 and b < 0 or a > 0 and b < 0

Case 1: (x – 1) < 0 and (x – 2) < 0

∴ x < `square` and x > `square`

Which is contradiction

Case 2: x – 1 and x – 2 < 0

∴ x > `square` and x < `square`

1 < `square` < 2

f(x) is decreasing if and only if x ∈ `square`

Find the equation of tangent and normal to the curve y = x² + 5 where the tangent is parallel to the line 4x – y + 1 = 0.

A function f is said to be increasing at a point c if ______.

If 0 < η < 1 then the demand is ______.

Determine the minimum value of the function.

f(x) = 2x³ – 21x² + 36x – 20

Evaluate the following : `int x^3.logx.dx`

Integrate the following w.r.t. x : `((3sin - 2)*cosx)/(5 - 4sin x - cos^2x)`

Evaluate the following.

`int 1/(x(x^6 + 1))` dx 

Evaluate the following.

`int 1/(4x^2 - 20x + 17)` dx

Evaluate the following.

`int x/(4x^4 - 20x^2 - 3) dx`

Evaluate the following.

`int 1/(7 + 6"x" - "x"^2)` dx

Evaluate the following.

`int "x"^2 *"e"^"3x"`dx

Evaluate:

`int (2x + 1)/(x(x - 1)(x - 4)) dx`.

Evaluate:

`int x/((x - 1)^2(x + 2)) dx`

`int "dx"/(("x" - 8)("x" + 7))`=

If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______

To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.

For `int ("x - 1")/("x + 1")^3  "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)².