Calculus math worksheets

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Change at an instant 11Limit notation 18Estimate limits from graphs 21Estimate limits from tables 24Algebraic properties of limits 35Evaluate limits by algebraic manipulation 48Squeeze theorem 26Types of discontinuity 35Continuity at a point and on an interval 36Infinite limits and asymptotes 46Intermediate value theorem 21

Average and instantaneous rate of change 80Derivative as a limit 12Estimate a derivative at a point 101Differentiability and continuity 54Power rule 181Constant, sum, and difference rules 34Derivatives of sine, cosine, exponential, and logarithmic functions 80Product rule 84Quotient rule 86Derivatives of remaining trigonometric functions 12

Chain rule 183Implicit differentiation 12Derivatives of inverse functions 16Derivatives of inverse trigonometric functions 10Higher-order derivatives 104

Interpret the derivative in context 39Straight-line motion 32Rates of change in applied contexts 67Related rates 10Linear approximation 45L'Hospital's rule 10

Mean value theorem 17Extreme value theorem and critical points 85Increasing and decreasing intervals 173First derivative test 111Candidates test for absolute extrema 28Concavity and inflection points 258Second derivative test 205Sketch a function from its derivatives 168Optimization 192Behavior of implicit relations 16Newton's method 47Bisection method 11

Accumulation of change 39Riemann sums 40Definite integral notation 37Accumulation functions 98Fundamental theorem of calculus 90Properties of definite integrals 65Antiderivatives and indefinite integrals 102Integration by substitution 61Long division and completing the square 36Integration by parts 43Partial fractions 34Improper integrals 52

Model with differential equations 69Verify solutions of differential equations 71Slope fields 77Separation of variables 73Particular solutions from initial conditions 72Exponential models 74Logistic models 56Euler's method 56

Average value of a function 45Motion from integrals 47Accumulation in applied contexts 100Area between curves 167Area between curves in terms of y 44Volumes with cross-sections 49Disc method 48Washer method 45Arc length 40

Differentiate parametric equations 66Second derivatives of parametric equations 68Arc length of parametric curves 68Vector-valued functions 77Integrate vector-valued functions 67Motion with parametric functions 70Polar derivatives 68Area of a polar region 62Area between two polar curves 56

Convergent and divergent series 68Geometric series 66The nth-term test 68Integral test 71Harmonic and p-series 67Comparison tests 67Alternating series test 68Ratio test 67Absolute and conditional convergence 69

Alternating series error bound 29Taylor polynomials 32Lagrange error bound 33Radius and interval of convergence 32Taylor and Maclaurin series 28Functions as power series 31

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