Calculus for Advanced Placement |
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... substituting the i.c. ( x , y ) = ( a , b ) . EXAMPLE : Solve the d.e. xy ́ + ( 1 - x ) y = e2x on I = ( 0 , + ∞ ) subject to the i.c. f ( 1 ) = 1 . SOLUTION : Dividing by x # 0 the equation becomes y ́ + ( -—- which is a first order ...
... substituting the i.c. ( x , y ) = ( a , b ) . EXAMPLE : Solve the d.e. xy ́ + ( 1 - x ) y = e2x on I = ( 0 , + ∞ ) subject to the i.c. f ( 1 ) = 1 . SOLUTION : Dividing by x # 0 the equation becomes y ́ + ( -—- which is a first order ...
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1+x² antiderivative approximation arc length arcsinx arctan argsinhx asymptote b₁ becomes c₁ calculate the area circle constant continuous function cose coshx curvature curve decreasing defined definition derivative differential equations directrix diverges domain dt dt dx dx ellipse endpoints EXAMPLE EXERCISES ON CHAPTER exists f is continuous formula function f graph hence hyperbolic functions improper integral indefinite integral interval a,b inverse inverse trigonometric functions l'Hôpital's rule lim f(x limit linear logarithmic mean value theorem NOTE obtain parabola parametric equations partial fractions partition polynomial of degree power series PROOF prove radius region bounded sequence series converges Similarly sinhx sinx slope solution subintervals tangent telescoping series trigonometric functions variable velocity volume write x-axis X-Xo x²+1 x²+2x+3 y-axis y-intercepts α α