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(Solved): Convert the following: (a) 300\deg to radians. (b) 135\deg to radians. (c) (5\pi )/(9) to degrees. ...
Convert the following:
(a) 300\deg to radians.
(b) 135\deg to radians.
(c) (5\pi )/(9) to degrees.
(d) (3\pi )/(10) to degrees.
Given that the total cost and total revenue functions of a firm are:
C(q)=0.02q^(3)-5q^(2)+1000q+500, and ,R(q)=1200q-0.01q^(3)
Use the Intermediate Value Theorem to prove that there are at least two production levels q
in 0,300 where the company breaks even.
Consider the function g(x)=(x^(2)+1)/(x+2) on the interval -1,2. Find the value of c guaranteed by
the Mean Value Theorem.
Evaluate the limit using L'Hôpital's Rule if necessary:
(a) \lim_(x->-4)(2x^(2)+13x+20)/(x+4)
(b) \lim_(x->\infty )\sqrt(x)e^(-x)
(c) \lim_(x->3)(\sqrt(x+1)-2)/(x^(3)-7x-6)
(d) \lim_(x->0)(e^(x)-1)/(sinx)
The number x of surfboards that a company will supply and their price p (in EC dollars) are
related by equation x^(2)=5p^(2)+12500.
(a) Find (dx)/((d)q) at p=100. (b) How would you interpret that answer?
Given the function 5q^(4)-3p^(2)q-2p^(3)=270, derive an expression for (dp)/((d)q).
A government imposes a tax on a good, and the demand function is given by: p^(2)q+2p=100,
where p is the price and q is the quantity demanded. If the price increases at a rate of 2
units per day. Use calculus to estimate how fast is the quantity demanded changing when
p=5 and q=6.
Find the Maclaurin series for the function f(x)=e^(x)sinx, up to the fourth degree.
Compute the Taylor series for the function f(t)=e^(2t) for t=1, up to the second degree.
The national debt of Handover (in billions of dollars) t years from now is given by the
function, N(t)=0.3+1.4e^(0.01t), find the relative rate of change of the debt 10 years from
now.
A local essential oil producer wants to increase her revenues by reducing the price of her
signature product. If the demand function for this product is q_(d)=60-3p, where p is the
price per bottle and q_(d) is the quantity demanded. Determine whether she will achieve the
goal with this sale.
Find the first derivative of the function f(x)=(2x^(4)+3x^(3)+7x+9)^(5x).
Find the first derivative of the function f(x)=ln((\root(3)((4x^(3)+7)^(2)))/((5x^(2)+9x)^(3)(x^(4)+6x)^(2))).
