Questions from General Calculus

Q: The Gateway Arch in St. Louis was designed by Eero Saarinen

The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation y = 211.49 - 20.96 cosh 0.03291765x for the central curve of the arch, where x and y are measured in...

Q: A telephone line hangs between two poles 14 m apart in the

A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 20 cosh(x/20) - 15, where x and y are measured in meters. (a) Find the slope of this curve where it meets the right...

Q: (a) Show that any function of the form y

(a) Show that any function of the form y = A sinh mx + B cosh mx satisfies the differential equation y’’ = m2y. (b) Find y = y(x) such that y’’ = 9y, y(0) = -4, and y’(0) = 6.

Q: If V is the volume of a cube with edge length x

If V is the volume of a cube with edge length x and the cube expands as time passes, find dV/dt in terms of dx/dt.

Q: Use implicit differentiation to find an equation of the tangent line to

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y2 (y2 – 4) = x2(x2 – 5), (0, -2), (devil’s...

Q: If x = ln(sec θ + tan θ), show

If x = ln(sec θ + tan θ), show that sec θ = cosh x.

Q: At what point of the curve y = cosh x does the

At what point of the curve y = cosh x does the tangent have slope 1?

Q: Investigate the family of functions fn(x) = tanh

Investigate the family of functions fn(x) = tanh (n sin x) where n is a positive integer. Describe what happens to the graph of fn when n becomes large.

Q: Show that if a ≠ 0 and b ≠ 0, then

Show that if a ≠ 0 and b ≠ 0, then there exist numbers α and β such that aex + be-x equals either α sinh(x + β) or α cosh(x + β) In other words, almost every function of the form f (x) = aex + be-x is...

Q: Find the numerical value of each expression. (a)

Find the numerical value of each expression. (a) sinh 0 (b) cosh 0