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Calculus
Suppose that 3 Joules of work is needed to stretch a spring from its natural length of 13 cm to a length of 36 cm. a) How much work is needed to stretch the spring from 16 cm to 30 cm?
b) How far (in meters) beyond its natural length would a force of 35 N keep the spring stretched?
b) How far (in meters) beyond its natural length would a force of 35 N keep the spring stretched?
Calculus
True or false? Please justify or give a counter example if you don't mind
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**If h'(a) = 0 for some a E (1; 3), then h has a local maximum or a local minimum at a.
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**If h'(a) = 0 for some a E (1; 3), then h has a local maximum or a local minimum at a.
Calculus
True or false? Please justify or give a counter example if you don't mind
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**If h has a local maximum at a 2 (1; 3), then h'(a) = 0.
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**If h has a local maximum at a 2 (1; 3), then h'(a) = 0.
Calculus
True or false? Please justify or give a counter example if you don't mind
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**g has at least one local extremum.
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**g has at least one local extremum.
Calculus
True or false? Please justify or give a counter example if you don't mind
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**There is some a E R such that g has a global maximum at a.
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**There is some a E R such that g has a global maximum at a.
Calculus
True or false? Please justify or give a counter example if you don't mind
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**There is some a E R with 1 < a < 3 such that f has a local minimum at a.
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is di erentiable, and that h(x) has domain (1; 3) and is differentiable.
**There is some a E R with 1 < a < 3 such that f has a local minimum at a.
Calculus
What is the derivative of cosh(3x^2+1)?
Calculus
Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 5 cubic feet per minute. If the pool has radius 7 feet and height 9 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 7 feet?
Calculus
The price (in dollars) p and the quantity demanded q are related by the equation: p^2+2q^2=1100.
If R is revenue, dR/dt can be expressed by the following equation: dR/dt=A (dp/dt),
where A is a function of just q.
A=
Find dR/dt when q=20 and dp/dt=3.
dR/dt=
If R is revenue, dR/dt can be expressed by the following equation: dR/dt=A (dp/dt),
where A is a function of just q.
A=
Find dR/dt when q=20 and dp/dt=3.
dR/dt=
Calculus
A price p (in dollars) and demand x for a product are related by
2x^2+1xp+50p^2=26000.
If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand.
Rate of change of demand =
2x^2+1xp+50p^2=26000.
If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand.
Rate of change of demand =
