Q: The angle of elevation of the sun is decreasing at a rate
The angle of elevation of the sun is decreasing at a rate of 0.25 rad/h. How fast is the shadow cast by a 400-ft-tall building increasing when the angle of elevation of the sun is π/6?
See AnswerQ: Evaluate dy if y = x3 - 2x2 + 1, x
Evaluate dy if y = x3 - 2x2 + 1, x = 2, and dx = 0.2.
See AnswerQ: A window has the shape of a square surmounted by a semi
A window has the shape of a square surmounted by a semi- circle. The base of the window is measured as having width 60 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate...
See AnswerQ: Express the limit as a derivative and evaluate. lim
Express the limit as a derivative and evaluate. lim ℎ→0 4 16+ℎ −2 ℎ
See AnswerQ: Suppose f is a differentiable function such that f (g(
Suppose f is a differentiable function such that f (g(x)) = x and f ‘(x) = 1 + [f(x)]2 . Show that g’(x) = 1 / (1 + x2).
See AnswerQ: Determine whether the statement is true or false. If it is
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If y = e2, then y’ = 2e.
See AnswerQ: The Michaelis-Menten equation for the enzyme chymotrypsin is
The Michaelis-Menten equation for the enzyme chymotrypsin is v = 0.14[S] / 0.015 + [S] where v is the rate of an enzymatic reaction and [S] is the concentration of a substrate S. Calculate dv/d[S] and...
See AnswerQ: Show that the length of the portion of any tangent line to
Show that the length of the portion of any tangent line to the astroid x2/3 + y2/3 = a2/3 cut off by the coordinate axes is constant.
See AnswerQ: Determine whether the statement is true or false. If it is
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. The derivative of a polynomial is a polynomia...
See AnswerQ: Show, using implicit differentiation, that any tangent line at a
Show, using implicit differentiation, that any tangent line at a point P to a circle with center O is perpendicular to the radius OP.
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