12th Maths | Exercise 7.8 Qn. No. 1 | Applications of Differential Calculus | TN New Syllabus
XII-Maths | Applications of Differential Calculus #PolarForm, #XIImaths, #Chapter7, #complexnumbers, #tnnewsyllabus 12th Maths | Chapter 7 | Applications of Differential Calculus | TN New Syllabus Class 12 Maths 7.2 Meaning of Derivatives 7.2.1 Derivative as slope Example 7.1 7.2.2 Derivative as rate of change Examples 7.2 to 7.6 7.2.3 Related rates Example 7.7 to 7.10 Exercise 7.1 7.2.4 Equations of Tangent and Normal Definition 7.1 & 7.2 Tangent & Normal Remark Slope 0 and infinity Example 7.11 to 7.13 7.2.5 Angle between two curves Example 7.14 to 7.18 Exercise 7.2 7.3 Mean Value Theorem Theorem 7.1 (Intermediate value theorem) 7.3.1 Rolle’s Theorem Theorem 7.2 (Rolle’s Theorem) Example 7.19 to 7.24 7.3.2 Lagrange’s Mean Value Theorem Theorem 7.3 (L.M.V Theorem) Example 7.25 7.3.3 Applications Example 7.26 to 7.29 Exercise 7.3 7.4 Series Expansions Theorem 7.5 (a. Taylor’s Series) (b. Maclaurin’s series) Example 7.30 to 7.32 Exercise 7.4 7.5 Indeterminate Forms 7.5.1 A Limit Process 7.5.2 The hospital’s Rule 7.5.3 Indeterminate forms Example 7.33 to 7.42 7.5.4 Indeterminate forms Example 7.43 to 7.45 Exercise 7.5 7.6 Applications of First Derivative 7.6.1 Monotonicity of functions Definition 7.4 & 7.5 increasing & decreasing. Theorem 7.7 Definition 7.6 (A stationary point) Definition 7.7 (A critical point) Example 7.46 & 7.47 7.6.2 Absolute maxima and minima Diagrams Theorem 7.8 (Extreme Value Theorem) Example 7.48 & 7.49 7.6.3 Relative Extrema on an Interval Theorem 7.9 (Fermat) 7.6.4 Extrema using First Derivative Test Theorem 7.10 (First Derivative Test) Example 7.50 to 7.56 Exercise 7.6 7.7 Applications of Second Derivative 7.7.1 Concavity,Convexity,Points of Inflection Theorem 7.11 (Test of Concavity) Definition 7.9 (Points of Inflection) Theorem 7.12 (Test for Points of Inflection) Example 7.57 & 7.58 7.7.2 Extrema using Second Derivative Test Theorem 7.13 (The Second Derivative Test) Example 7.59 to 7.61 Exercise 7.7 7.8 Applications in Optimization Example 7.62 to 7.65 Exercise 7.8 7.9 Symmetry and Asymptotes 7.9.1 Symmetry 7.9.2 Asymptotes Example 7.66 to 7.68 7.10 Sketching of Curves
