Calculus with Analytic GeometryFunctions and limits; The derivative; Applications of the derivative; The integral; Applications of the integral; Transcedental functions; Techniques of integration; Indeterminate forms and improper integrals; Numerical methods, approximations; Infinite series; Conics and polar coordinates; Geometry in the plane, vectors; Geometry in space, vectors; The derivative in n-space; The integral in n-space; Vector calculus; Differential equations. |
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Results 1-3 of 83
Page 47
... constant function f ( x ) = 4 FIGURE 9 4 3 2 1 1 2 3 4 5 Χ The identity function f ( x ) = x FIGURE 10 PROBLEM SET 2.2 PARTIAL CATALOGUE OF FUNCTIONS A function of the form f ( x ) = k , where k is a constant ( real number ) is called a ...
... constant function f ( x ) = 4 FIGURE 9 4 3 2 1 1 2 3 4 5 Χ The identity function f ( x ) = x FIGURE 10 PROBLEM SET 2.2 PARTIAL CATALOGUE OF FUNCTIONS A function of the form f ( x ) = k , where k is a constant ( real number ) is called a ...
Page 100
... CONSTANT AND POWER RULES The graph of the constant function f ( x ) = k is a horizontal line ( Figure 1 ) which , therefore , has slope zero everywhere . This is one way to understand our first theorem . FIGURE 1 y X f ( x ) = ( x + h ...
... CONSTANT AND POWER RULES The graph of the constant function f ( x ) = k is a horizontal line ( Figure 1 ) which , therefore , has slope zero everywhere . This is one way to understand our first theorem . FIGURE 1 y X f ( x ) = ( x + h ...
Page 101
... constant multiples of functions or to sums of functions . Theorem D ( Constant Multiple Rule ) . If k is a constant and ƒ is a differentiable func- tion , then ( kf ) ' ( x ) = k⋅ f ' ( x ) —that is , D [ k ⋅f ( x ) ] = k · Df ( x ) ...
... constant multiples of functions or to sums of functions . Theorem D ( Constant Multiple Rule ) . If k is a constant and ƒ is a differentiable func- tion , then ( kf ) ' ( x ) = k⋅ f ' ( x ) —that is , D [ k ⋅f ( x ) ] = k · Df ( x ) ...
Contents
Preliminaries | 1 |
Functions and Limits | 36 |
The Derivative | 86 |
Copyright | |
17 other sections not shown
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angle antiderivative approximate bounded C₁ C₂ calculate Cartesian Chain Rule Chapter Review Problems circle constant continuous converges corresponding cos² cosh curve cylinder definite integral derivative differential equation distance diverges domain dx dy dy dx ellipse Evaluate EXAMPLE 3 Find False Find the area Find the equation Find the volume formula function f given Green's Theorem Hint hyperbola intersection interval iterated integral l'Hôpital's Rule length lim f(x lim h→0 limit maximum Mean Value Theorem minimum value obtain parabola parametric equations perpendicular plane polynomial PROBLEM SET Proof radians radius rational number real numbers region result revolved Riemann sum sec² Section Show shown in Figure sin² sinh Sketch the graph slope solid solve Suppose surface tangent line True variable vector velocity vertical x-axis x₁ xy-plane y-axis zero