Find the present and future values of a constant income stream of $3000 per year over a 13 year period at 5% annual interest compounded continuously. Round your answers to the nearest cent. In particular, ROUND your answer for the Present Value to the nearest cent BEFORE using it to compute the Future Value.
a) Present Value: $
equation editor
b) Future Value: $
equation editor
In: Math
a) Evaluate the limit lim x→0 tan(2x) / x
b) Differentiate y = x^tan(x)
c) Find the equation of the tangent line to 4x^2 + 2xy−y^2 = 4 at the point (1, 2).
d) Differentiate f(x) = arctan(x^2 + 1)
e) Differentiate f(x) = ln(cosh x)
Thank you!
In: Math
(a) Find the exact length of the curve y = 1/6 (x2 + 4)(3/2) , 0 ≤ x ≤ 3. (b) Find the exact area of the surface obtained by rotating the curve in part (a) about the y-axis.
I got part a I NEED HELP on part b
In: Math
7) Determine the equations of the lines tangent to the
graph of 9?2 + 4?2 + 18? − 16? − 11 = 0 at the points where x = 0.
Where do these two lines
intersect?
In: Math
Find an equation of the tangent line to the curve cos ( x ) + 11 y ^2 = x y ^3 + 34 at the point ( 0 , √ 3 ) . Assume that y is a function of x . Express all numbers in exact form and write the equation of the tangent line in terms of x and y .
In: Math
The function F(x) = x2 - cos(π x) is defined on the interval 0 ≤ x ≤ 1 radians. Explain how the Intermediate Value Theorem shows that F(x) = 0 has a solution on the interval 0 < x < .
In: Math
Consider a continuous, integrable, twice-differentiable function
f with input variable x.
In terms of the units of f and the units of x, choose the units of
each function or expression below:
(a) The units of f ' are
the units of
f
the units of
x
(the units of f)(the units of x
)
| the units of f |
| the units of x |
| the units of f |
| (the units of x)2 |
| the units of f |
| (the units of x)3 |
(b) The units of f '' are
the units of
f
the units of
x
(the units of f)(the units of x
)
| the units of f |
| the units of x |
| the units of f |
| (the units of x)2 |
| the units of f |
| (the units of x)3 |
(c) The units of
| b | f(x)dx |
| a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
| the units of f |
| the units of x |
| the units of f |
| (the units of x)2 |
| the units of f |
| (the units of x)3 |
(d) The units of
| b | f '(x)dx |
| a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
| the units of f |
| the units of x |
| the units of f |
| (the units of x)2 |
| the units of f |
| (the units of x)3 |
(e) The units of
| n | f(xi)Δx |
| i=1 |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
| the units of f |
| the units of x |
| the units of f |
| (the units of x)2 |
| the units of f |
| (the units of x)3 |
(f) The units of
| f(b)−f(a) |
| b−a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
| the units of f |
| the units of x |
| the units of f |
| (the units of x)2 |
| the units of f |
| (the units of x)3 |
(g) The units of
| d |
| dx |
| x | f(t)dt |
| a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
| the units of f |
| the units of x |
| the units of f |
| (the units of x)2 |
| the units of f |
| (the units of x)3 |
(h) The units of
| d2 |
| dx2 |
| x | f(t)dt |
| a |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
| the units of f |
| the units of x |
| the units of f |
| (the units of x)2 |
| the units of f |
| (the units of x)3 |
(i) The units of h in
| f(a+h)−f(a) |
| h |
are
the units of
f
the units of
x
(the units of
f
)(the units of
x
)
| the units of f |
| the units of x |
| the units of f |
| (the units of x)2 |
| the units of f |
| (the units of x)3 |
In: Math
The principal value of tan-1(tan 3π/5) is _____________.
(a) 2π/5
(b) -2π/5
(c) 3π/5
(d) -3π/5
In: Math
Find the area enclosed by the curves, x + y = 8 and x = y^2 − 4y + 4.
In: Math
Use the Divergence Theorem ∬SF⋅dS=∭D∇⋅FdV to find ∬SF⋅dS where F(x,y,z)=x^2i+y^2j+z^2k and S S is the surface of the solid bounded by x^2+y^2=9 , z = 0 , and z=6
In: Math
*Calc 3 multivariable question*
Find the surface area of paraboloid z=3-2x2-2y2
the paraboloid lies above the xy plane
In: Math
Partial Fractions: Problem 2
Use the method of partial fraction decomposition to write the following rational expression as the sum of simpler rational functions whose denominators are polynomials of degree 1.
−20x+20/x^2−x−56=
In: Math
Find the solution of the Cauchy problem for the differential equationy" + 2y' + y = e–x cos x
subject to the initial conditions: y(0) = 0, y'(0) = 1.
Verify the solution obtained by direct substitution into the
equation and confirm that it satisfies the initial condition.
In: Math
A certain capsule is designed to release a drug at a rate of r(t) = 4te−2t units per minute. If the capsule is ingested at t = 0
find a formula for the amount of drug that has been released at t = T .
In: Math
Five years ago, peter was three times as old as alex. if at the present time alex is ten years old, how old will peter be in the next three years?
In: Math