Q: Suppose the curve y = x4 + ax3 + bx2 + cx
Suppose the curve y = x4 + ax3 + bx2 + cx + d has a tangent line when x = 0 with equation y = 2x + 1 and a tangent line when x = 1 with equation y = 2 – 3x. Find the values of a, b, c, and d.
See AnswerQ: (a). Suppose the horizontal distance between P and Q is
(a). Suppose the horizontal distance between P and Q is 100 ft. Write equations in a, b, and that will ensure that the track is smooth at the transition points. (b). Solve the equations in part (a) fo...
See AnswerQ: State each differentiation rule both in symbols and in words.
State each differentiation rule both in symbols and in words. (a). The Power Rule (b). The Constant Multiple Rule (c). The Sum Rule (d). The Difference Rule (e). The Product Rule (f). The Quotient...
See AnswerQ: Certain combinations of the exponential functions, ex and e-x
Certain combinations of the exponential functions, ex and e-x arise so frequently in mathematics and its applications that they deserve to be given special names. This project explores the properties...
See AnswerQ: The tangent line approximation L (x) is the best first
The tangent line approximation L (x) is the best first-degree (linear) approximation f (x) to near x = a because f (x) and L (x) have the same rate of change (derivative) at a. For a better approximat...
See AnswerQ: Bézier curves are used in computer-aided design and are named
Bézier curves are used in computer-aided design and are named after the French mathematician Pierre Bézier (1910–1999), who worked in the automotive industr...
See AnswerQ: Find numbers a and b such that limx→1 √ax
Find numbers a and b such that limx→1 √ax + b – 2/x = 1
See AnswerQ: Show that d/dx (sin2 x/ 1 + cot
Show that d/dx (sin2 x/ 1 + cot x + cos2x/1 + tan x) = -cos 2x
See AnswerQ: If f (x) = limt→x sec t –
If f (x) = limt→x sec t – sec x/t - x, find the value of f'(π/4).
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