Questions from General Calculus

Q: If g(x) + x sin g(x)

If g(x) + x sin g(x) = x2, find g’(0).

Q: Brain weight B as a function of body weight W in fish

Brain weight B as a function of body weight W in fish has been modeled by the power function B = 0.007W2/3, where B and W are measured in grams. A model for body weight as a function of body length L...

Q: Two sides of a triangle have lengths 12 m and 15 m

Two sides of a triangle have lengths 12 m and 15 m. The angle between them is increasing at a rate of 2º /min. How fast is the length of the third side increasing when the angle between the sides of f...

Q: Which of the following areas are equal? Why?

Which of the following areas are equal? Why?

Q: A mass on a spring vibrates horizontally on a smooth level surface

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = 8 sin t, where t is in seconds and x in centimeters. (a) Find the velocity and acc...

Q: (a) Draw the line y = 2t + 1 and

(a) Draw the line y = 2t + 1 and use geometry to find the area under this line, above the t-axis, and between the vertical lines t = 1 and t = 3. / //

Q: For any vectors u and v in V3, u ∙ v

For any vectors u and v in V3, u ∙ v = v ∙ u.

Q: For any vectors u and v in V3, u × v

For any vectors u and v in V3, u × v = v × u.

Q: For any vectors u and v in V3 and any scalar k

For any vectors u and v in V3 and any scalar k, K (u ∙ v) = (ku) ∙ v

Q: For any vectors u and v in V3 and any scalar k

For any vectors u and v in V3 and any scalar k, K (u × v) = (ku) × v