HSC Commerce Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Evaluate the following:

\[\lim_{x->∞} \frac{2x + 5}{x^2 + 3x + 9}\]

Evaluate the following:

`lim_(x->∞) (sum "n")/"n"^2`

Evaluate the following:

`lim_(x->0) (sqrt(1+x) - sqrt(1-x))/x`

Evaluate the following:

`lim_(x->a) (x^(5/8) - a^(5/8))/(x^(2/3) - a^(2/3))`

Evaluate the following:

`lim_(x->0) (sin^2 3x)/x^2`

If `lim_(x->a) (x^9 + "a"^9)/(x + "a") = lim_(x->3)` (x + 6), find the value of a.

If `lim_(x->2) (x^n - 2^n)/(x-2) = 448`, then find the least positive integer n.

If f(x) = `(x^7 - 128)/(x^5 - 32)`, then find `lim_(x-> 2)` f(x)

Let f(x) = `("a"x + "b")/("x + 1")`, if `lim_(x->0) f(x) = 2` and `lim_(x->∞) f(x) = 1`, then show that f(-2) = 0

Examine the following function for continuity at the indicated point.

f(x) = `{((x^2 - 4)/(x-2) "," if  x ≠ 2),(0 "," if x = 2):}` at x = 2

Examine the following function for continuity at the indicated point.

f(x) = `{((x^2 - 9)/(x-3) "," if  x ≠ 3),(6 "," if x = 3):}` at x = 3

Show that f(x) = |x| is continuous at x = 0.

Find the derivative of the following function from the first principle.

x²

Draw the network for the project whose activities with their relationships are given below:

Activities A, D, E can start simultaneously; B, C > A; G, F > D, C; H > E, F.

Find the derivative of the following function from the first principle.

log(x + 1)

Draw the event oriented network for the following data:

Construct the network for the projects consisting of various activities and their precedence relationships are as given below:

A, B, C can start simultaneously A < F, E; B < D, C; E, D < G

Construct the network for each the projects consisting of various activities and their precedence relationships are as given below:

Construct the network for the project whose activities are given below.

Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity. Determine the critical path and the project completion time.

Find the derivative of the following function from the first principle.

e^x