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## Unit 6: Calculus

#### Learning Contents

1. Limits and continuity: limits of a function indeterminate forms, algebraic properties of limits (without proof), Basic theorems on limits of algebraic,trigonometric, exponential and logarithmic functions, continuity of a function, types of discontinuity, graphs of discontinuous function.
2. Derivatives: derivative of a function, derivatives of algebraic, trigonometric, exponential and logarithmic functions by definition (simple forms), rules of differentiation. derivatives of parametric and implicit functions, higher order derivatives, geometric interpretation of derivative, monotonicity of a function, interval of monotonicity, extreme of a function, concavity, points of inflection, derivative as rate of measure.
3. Anti-derivatives: anti-derivative. integration using basic integrals, integration by substitution and by parts methods, the definite integral, the definite integral as an area under the given curve, area between two curves

#### Learning Outcomes

1. define limits of a function.
2. identify indeterminate forms.
3. apply algebraic properties of limits.
4. evaluate limits by using theorems on limits of algebraic, trigonometric, exponential and logarithmic functions.
5. define and test continuity of a function.
6. define and classify discontinuity.

7. interpret derivatives geometrically.
8. find the derivatives, derivative of a function by first principle (algebraic, trigonometric exponential and logarithmic functions).
9. find the derivatives by using rules of differentiation (sum, difference, constant multiple, chain rule, product rule, quotient rule, power and general power rules).
10. find the derivatives of parametric and implicit functions.
11. calculate higher order derivatives.
12. check the monotonicity of a function using derivative.
13. find extreme values of a function.
14. find the concavity of function by using derivative.

15. define integration as reverse of differentiation.
16. evaluate the integral using basic integrals.
17. integrate by substitution and by integration by parts method.
18. evaluate the definite integral.
19. find area between two curves.