Math Practice Quiz for Class 11 (Nepal, Kathmandu Valley)

Limits

• The limit of a function f(x) as x approaches a certain value can be found by plugging in that value into the function.
• For example, the limit of f(x) = 3x^2 - 2x + 5 as x approaches 2 can be found by plugging in x = 2 into the function.

Derivatives

• The derivative of a function g(x) represents the rate of change of the function with respect to x.
• The derivative of g(x) = 4x^3 - 3x^2 + 2x - 7 can be found by applying the power rule and sum rule of differentiation.

Standard Deviation

• The standard deviation of a set of data is a measure of the spread or dispersion of the data.
• The standard deviation of the set {5, 8, 12, 15, 18} can be calculated using the formula for standard deviation.
• The standard deviation of the set {4, 4, 4, 4, 4, 4, 4, 4, 4, 14} is affected by the outlier value of 14.

Continuity of a Function

• Continuity of a function at a point means that the function is defined at that point and the limit of the function as x approaches that point exists and is equal to the function value at that point.
• Continuity is an important concept in calculus and is used to define differentiability.

Composite Functions

• The derivative of a composite function f(g(x)) can be found using the chain rule of differentiation.
• For example, the derivative of f(g(x)) where f(x) = |x + 2| and g(x) = 1/x can be found by applying the chain rule and power rule of differentiation.