Patterns of problems

## Limits And Derivatives

- Understand the patterns for better solving
1
Pattern: Identifying the limit of a function from its graph
Description: To do so, check the neighborhood carefully by observing the graph. Take care of all the probabilities when approaching from the left side and the right side .
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2
Pattern: Finding the limit using the conditions given on the function
Description: Both left hand limit and right hand limit should be evaluated and equated in order to find the limit of the function existing at a given point.
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3
Pattern: Identifying the different indeterminate forms.
Description: There are 7 indeterminate forms in particular. Substitute the given value in the variable to find out the indeterminate form.
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4
Pattern: Identify and understand the properties of algebra of limits.
Description: The statements can be proved false by giving counter examples.
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5
Pattern: Finding derivative of given function using and sum and difference rule.
Description: Differentiate the function using the sum and difference rules of derivatives.
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6
Pattern: Identify and solve problems using product rule for two functions (Leibnitz rule).
Description: Identify the two functions u and v in the given function and apply the product rule to find the derivative of the given function.
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7
Pattern: Identify and solve problems using quotient rule.
Description: Identify u and v in the given function and use the quotient rule to find the derivative of the given function.
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