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A. The derivative of f(x)=(5x3+4)(6ln(x)-2x) B. The derivative of c(x)=ln(4x3-x2)
a) Determine all x-values where the function has a horizontal tangent line. y=ln(1+sinx) b) The position...
At what point does the normal to y= (-1)+(4x^2) at (1,3) intersect the parabola a SECOND...
If x^3 +y^3 = 28, find the value of d^2y/dx^2 at the point (1,3).
Consider the ellipse r(t) =〈3 cos(t),4 sin(t)〉, for 0 ≤ t ≤ 2π. (a) At what...
Apply Lagrange multipliers to solve the problem. Find the dimensions of the box with a volume...
Find equations of the tangent lines to the curve y = x − 1/x + 1...
a. 6. Complete the following steps: i. Graph the point P(6, -2) ii. Graph another point...
A bakery works out a demand function for its chocolate chip cookies and finds it to...
A spherical tank with radius 2m is half full. Set up, but DO NOT evaluate, an...
Use the Laplace transform to solve the following initial value problem, y′′ − 8y′ − 9y ...
Sketch the graphs of the quadratics surfaces defined by the equations x = z2 - y2...
1. Find the radius of convergence for: ∞∑n=1 (n!)^2 x^n /(2n)! 2. Find all the values of...
The table below shows values for four differentiable functions. Suppose we know the following things: h'(x)...
find laplace transform without using known transform: f(t)=at+bcos(2t)
Find the curvature, k(t), of the following: r(t) = t i + t^2 j + e^t...
1. Find the derivative of the function. y = e−8/x 2. Find the derivative of the...
b) i) Find the residues of the function ?(?) = ?2+1 ?(?−6) at its poles in...
Suppose that f is a differentiable function and define g(x)=e^(2*f(x)+5x). Suppose that f(-2) = 1 and...
Consider the graph y=6x^(1/5)+x^(6/5) Determine: a) interval(s) on which it is increasing b) interval(s) on which...
Evaluate ∫ ?−2 / [(2?−1)^2 * (?−1)] ?x
Two motorcycles, travelling at the same speed, approach an intersection, one from the north and the...
A conical tank is 14m high and its diameter across the top is 10m. Water is...
Determine the equation of the normal to y2 = (x3/2-x) at the point (1,-1). [ANSWER: y...
Given the given cost function C(x)=2600+590x+1.2x2 and the demand function p(x)=1770 Find the production level that...
find the derivative of the functions T(theta)=cos(theta^2 + 3theta - 10) f(x)=(3x/(x^2-1))^3/2
2. Suppose that F(x,y) is a conservative vector field with potential function f(x,y). Suppose that every...
find the equation of a tangent line(s) to the curve with slope 5 f(x)=x^3 + 3x^2...
a) Let y be the solution of the equation y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition y...
1. Find and interpret f'(−2) f(x)=−2x^2−3x+4 f'(-2)= 2. Find and interpret f'(1)and f′'(1) f(x)= 2/x f'(1)=...
Calculate the trapezoidal sum for the function f ( x ) = x^ 2 over the...
Given: Sigma (infinity) (n=1) sin((2n-1)pi/2)ne^-n Question: Determine if the series converges or diverges Additional: If converges,...
find the derivative using a definition of the derivative (h) of the following function f(x)= x/(x-1)
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an...
Compute the following derivative of ?(?, ?)=cos(?^4+?^6) (Use symbolic notation and fractions where needed.) ????=
Solve the following initial value problem: x2y′′+xy′−9y=0; y(1) = 6; y′(1) = 12
Find the probabilities of the following. a) If a dice is rolled then find the probability...
Find the minimum sum of 9x + 5y + 3z + 8 if x, y, and...
Find an equation for the tangent plane to: z=arctan(x^3y^2)z at P=(-1,-2,-1.326) .
A particle is located at the point (5, 5) on a metal surface whose temperature at...
For which values of p does ∞ n = 1 n7 (n8 + 7)9p converge? (Enter...
Use Implicit Differentiation to find first dy/dx , then the equation of the tangent line to...
Hiromi took a 250 mg dose of a pain killer before going to bed last night....
Consider the parallelepiped with adjacent edges u=6i+3j+k v=i+j+6k w=i+5j+4k Find the volume. V=
Let u=〈5,-1,6〉, v=〈0,1,2〉, and w=〈1,3,4〉. Find (a)u×(v×w) (b)(u×v)×w (c)(u×v)×(v×w) d)(v×w)×(u×v).
As we near the end of the term, it is important to acknowledge the ways you...
1) Suppose the cost in dollars of manufacturing q item is given by: C= 2000q +...
Consider the following initial value problem. y′ + 5y = { 0 t ≤ 2 10...
Consumers' Surplus The demand function for a certain make of replacement cartridges for a water purifier...
Use derivatives of transforms to evaluate the given Laplace transform. (Write your answer as a function...
The owner of a mid-size company advertises on the radio and in a newspaper. He has...
Let LaTeX: C(x)C ( x ) be the cost in dollar of manufacturing x items. If...
What are the equations of the tangent and normal lines to the following curve: y2+y+x =...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
Find the Taylor polynomial of degree 4, p4(x), about 0 for the function y = e^[x^(2)]....
1. The Taylor series for f(x)=x^3 at 1 is ∞∑n=0 cn(x−1)^n. Find the first few coefficients....
The rate of change in number of items sold is given by ?(?) = −31x^2 +...
a- what is the difference between the derivative of X^n and y^n (explain the followings: how...
Compute the work required to drain, from the top, a cylindrical water tank, with height =...
Given the function f(?) = ?^3 − 9?^2 + 24? − 2, a) Find the critical...
The supply curve for a commodity has the equation p = 0.4 x − 2.5 ,...
Use cylindrical coordinates. Evaluate 6(x3 + xy2) dV, where E is the solid in the first...
.Given: f '(x) = x^2 (x-1) (x-2), a) Find three first order critical values of f(x)....
1. Test the series below for convergence using the Root Test. ∞∑n=1 (4n/10n+1)^n The limit of...
Find the function f(x) such that f′′(x)=12x^2− 2/x^2 and f(1) = 5, f′(1) = 2
a) evaluate the directional derivative of z=F(x,y) = sin(xy) in the direction of u=(1,-1) at the...
Find the dimensions of a rectangle of perimeter 124cm with the largest possible area. (draw the...
A manufacturer estimates that when q thousand units of a particular commodity are produced each month,...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
1. For the following functions, find ∆y (the exact change) and dy (the approximate change from...
The supply equation for a certain tee shirt is x = 3p2 + 2p where p...
Find absolute minimum and maximum of the function F(x)=x^3+x^2-x+2 on closed interval (-3,0)
Use the definition of the Laplace transform to find the transform of: f(t)= at+ b cos(2t),...
The revenue and expense equation for widgets are revenue=100∗quantity−0.3∗quantity^2+0.004∗quantity^3 expense=600+10∗quantity Find the derivative of revenue with...
y^''-4y^'+5y=50xe^-x
A company's revenue from selling x items is given by the function R(x)=44x and it's from...
Let y=300∗1.84^x+250x and z=y^2+y. Find dz/dx when x=6.
Find the volume of the solid obtained by rotating the region bounded by the given curves...
Verify that the function ϕ(t)=c1e^−t+c2e^−2t is a solution of the linear equation y′′+3y′+2y=0 for any choice...
1. Find lim x-0. tan4x/sin5x 2. Find and simplify ?/(?) ?? ?(?) = 1-cos(?)/1+cos(?)
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