Questions from General Calculus

Q: Calculate y’. y = ln (cosh 3x)

Calculate y’. y = ln (cosh 3x)

Q: Calculate y’. y = cosh-1 (sinh x

Calculate y’. y = cosh-1 (sinh x)

Q: Find all values of c such that the parabolas y = 4x2

Find all values of c such that the parabolas y = 4x2 and x = c + 2y2 intersect each other at right angles.

Q: If g(θ) = θ sin θ, find g’’

If g(θ) = θ sin θ, find g’’(π/6).

Q: Fanciful shapes can be created by using the implicit plotting capabilities of

Fanciful shapes can be created by using the implicit plotting capabilities of computer algebra systems. (a) Graph the curve with equation y( y2 – 1)(y – 2)d = x(x – 1)(x – 2) At how many points does...

Q: Find y’’ if x6 + y6 = 1.

Find y’’ if x6 + y6 = 1.

Q: Find f(n)(x) if f (x)

Find f(n)(x) if f (x) = 1/(2 – x).

Q: Use mathematical induction (page 72) to show that if

Use mathematical induction (page 72) to show that if f (x) = xex, then f(n)(x) = (x + n)ex. Mathematical Induction In proving statements that involve a positive integer n, it is frequently helpful to...

Q: Find an equation of the tangent to the curve at the given

Find an equation of the tangent to the curve at the given point. y = 4 sin2x, (π/6, 1)

Q: Find equations of the tangent line and normal line to the curve

Find equations of the tangent line and normal line to the curve at the given point. x2 + 4xy + y2 = 13, (2, 1)