The Calculus with Analytic Geometry, Volume 1Harper & Row, 1981 - Calculus |
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Page 58
... Formulas similar to ( 4 ) and ( 10 ) for the sine of the sum and differ- ence of two numbers follow easily . A formula for the sine of the sum of two numbers is obtained from ( 10 ) and ( 11 ) . From ( 11 ) , sin ( a + b ) = COS ( π ...
... Formulas similar to ( 4 ) and ( 10 ) for the sine of the sum and differ- ence of two numbers follow easily . A formula for the sine of the sum of two numbers is obtained from ( 10 ) and ( 11 ) . From ( 11 ) , sin ( a + b ) = COS ( π ...
Page 61
... formula ( 23 ) by using formula ( 22 ) . 21. Derive formula ( 24 ) by using formula ( 21 ) . 22. Derive formula ( 25 ) by using formula ( 20 ) . 23. Derive a formula for sin 3t in terms of sin t by using formulas ( 12 ) , ( 14 ) , ( 15 ) ...
... formula ( 23 ) by using formula ( 22 ) . 21. Derive formula ( 24 ) by using formula ( 21 ) . 22. Derive formula ( 25 ) by using formula ( 20 ) . 23. Derive a formula for sin 3t in terms of sin t by using formulas ( 12 ) , ( 14 ) , ( 15 ) ...
Page 541
... formula ( 17 ) , f ' ( x ) = - 2 sin 2x 1 cos2 2x - Du u # 0 ( 20 ) = tanh - 1 ( cos 2x ) . = - 2 sin 2x sin2 2x ... formula of this section . 3. Formula ( 8 ) 4. Formula ( 10 ) 7. Formula ( 17 ) 8. Formula ( 18 ) 5 . Formula ( 11 ) 6 ...
... formula ( 17 ) , f ' ( x ) = - 2 sin 2x 1 cos2 2x - Du u # 0 ( 20 ) = tanh - 1 ( cos 2x ) . = - 2 sin 2x sin2 2x ... formula of this section . 3. Formula ( 8 ) 4. Formula ( 10 ) 7. Formula ( 17 ) 8. Formula ( 18 ) 5 . Formula ( 11 ) 6 ...
Common terms and phrases
absolute maximum value absolute minimum absolutely convergent antiderivative chain rule closed interval convergent coordinates cos² cosh cost function curve defined by f(x definite integral derivative differentiable directrix distance Draw a sketch elements of area ellipse evaluate Example exists f is continuous FIGURE Find an equation Find the area Find the volume focus following theorem formula function defined function f Given f(x graph of ƒ Hence hyperbola ILLUSTRATION intersection inverse L'Hôpital's rule lim f(x Limit Theorem measure natural logarithmic obtain open interval parabola particle perpendicular polar positive number power series Proof Prove radius real numbers rectangle rectangular elements region bounded relative maximum value revolving Riemann sum sec² sequence shown in Fig Simpson's rule sin² sinh slope solid of revolution Solution square units tangent line tank velocity vertex vertices x₁ y₁