Podcast
Questions and Answers
What is the limit of $f(x) = 3x^2 - 2x + 5$ as $x$ approaches 2?
What is the limit of $f(x) = 3x^2 - 2x + 5$ as $x$ approaches 2?
What is the derivative of $g(x) = 4x^3 - 3x^2 + 2x - 7$?
What is the derivative of $g(x) = 4x^3 - 3x^2 + 2x - 7$?
What is the standard deviation of the set {5, 8, 12, 15, 18}?
What is the standard deviation of the set {5, 8, 12, 15, 18}?
Which of the following is the correct definition of continuity of a function?
Which of the following is the correct definition of continuity of a function?
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What is the standard deviation of the set {4, 4, 4, 4, 4, 4, 4, 4, 4, 14}?
What is the standard deviation of the set {4, 4, 4, 4, 4, 4, 4, 4, 4, 14}?
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If $f(x) = |x + 2|$ and $g(x) = rac{1}{x}$, what is the derivative of $f(g(x))$?
If $f(x) = |x + 2|$ and $g(x) = rac{1}{x}$, what is the derivative of $f(g(x))$?
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Study Notes
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.
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Description
Test your knowledge of limit and continuity, derivatives, integers, and standard deviation with this practice quiz designed for Class 11 students in Nepal's Kathmandu Valley.
