4x6 +31x+42x4 find xt +x³ – 30x² Given f(x) = 1. any horizontal asymptotes of f(x) algebraically using the calculus techniques discussed in class (no shortcuts!). If there are no horizontal asymptotes, state so AND describe any infinite behavior using limit notation. 2. the x-values of any holes of f(x) algebraically. Remember to show your work.

Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint g(x,y)=2x2+y2=...

Q: Solve  y" - 25y = 0

A: Given: y''-25y=0  

Q: Graph the ellipse and locate the foci: 9x2 + 4y2 - 18x + 8y - 23 = 0

A: Given:            9x2+4y2-18x+8y-23=0 Find the general form of the conic.          9x2+4y2-18x+8y-23...

Q: In Exercises 36-41, use the Root Test to determine convergence or divergence ( or state that the tes...

A: Given- ∑k=0∞k3k+1k To use- The Root Test to determine convergence or divergence.  

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 25x2 +...

A: 16y2+200x-160y+400=0 Differentiating with respect to x implicitly 50x+32ydydx+200-160dydx+0=0 32y-16...

Q: Use integration by parts to prove the reductionformula.

A:

Q: Use Formula 6 to graph the given functions on acommon screen. How are these graphs related?   y = lo...

A: We have to graph the function y=log2x, y=log4x, y=log6x, and y=log8x on the same screen.

Q: Graph of a linear function Find and graph the linear function that passes through the points 12, -32...

A: Equation of a line passes through x1, y1 and x2, y2 is y-y1=mx-x1Where slope m=y2-y1x2-x1

Q: -p? Suppose the demand for a certain brand of a product is given by D(p) = 207 + 150, where p is the...

A: The demand function is Dp=-p2207+150 where p is the price in dollars. Now, the price is defined as p...

Q: Apply the law of cosines to the triangle in the accompanying figure to derive the formula for cos (A...

A: Solution:-  Here we have to apply the Law of cosines to the triangle and derive the formula for  cos...

Q: Find the derivative of the function. 6. s(t) = 49 (6t - 7) %3D s'(t) =D %3D

A: Use the formula for derivative of a power of a function.

Q: The relationship between f and g is given. Explain the relationship between     f′ and g′. g(x) = −5...

A: Given relationship between f(x) and g(x) is - g(x) =-5f(x)            ...............(1)Differentiat...

Q: Sketch a graph of a function ƒ that is continuous on (- ∞, ∞) and has the following properties. ƒ'(x...

A: To sketch the graph if a function f which is continuous on (-∞, ∞)  and first and second derivatives...

Q: Find the period of the function y = 5 tan 2x

A: Given: y=5tan2x we know that period of tankx is πk similarly, period of given function will be π2

Q: Find the volume of the described solid S A pyramid with height  h and base an equilateral trianglewi...

A: To find the volume of the pyramid with height h and base an equilateral triangle with side a

Q: Given, f(x) = -5x4 + 4x3 - 19x2 + 16x + 4, shown (see attached) incomplete graphs of given polynomia...

A: The function f(x)=-5x4+4x3-19x2+16x+4. We have to find all the zeros of each function. Also, without...

Q: Divide (18x4 + 9x3 + 3x2)/(3x2 + 1)using long division. State the quotient,q(x), and the remainder, ...

A: Given - Dividient = 18x4+9x3+3x2Divisor = 3x2+1Dividing - 3x2+1 ) 18x4+9x3+3x2 ( 6x2+3x-1           ...

Q: Integrate ∫x(√4 − x )dx (a) by parts, letting dv =( √4 − ) dx. (b) by substitution, letting u = 4 − ...

A: Consider the integrals, ∫x4-xdx                                                                     ...

Q: Find the standard form of the equation of the ellipse with the given characteristics.   Center: (0, ...

A: Center of the ellipse = (h, k) = 0, 1Focus of the ellipse = 4, 1Vertex of the ellipse = 6, 1General ...

Q: Find a and b such that f is differentiable everywhere.

A: The given piecewise function is: fx=ax3,      x≤2x2+b,   x>2 This function is differentiable ever...

Q: State true or false  0 > -13

A: Given:0>-13

Q: Find the length and the cuur vature of the Smooth eurve rCt) = (snt)i t(5 cost); + (sint)K from o to...

A: Given curve is rt→=sinti+2costj+sintk and given t from 0 to 2π We have to find the length and curvat...

Q: In an oil refinery, a storage tank contains 2000 gal of gasoline that initially has 100 lb of an add...

A: We know that, dydt=Inflow rate - y(t)v(t)(outflow rate) According to the question v=2000 gal+40 galm...

Q: Find the mass of the following thin bars with the given density function. r1x2= 1 + x3, for 0 … x … ...

A: It is given that, r(x)= 1 + x3, for 0 … x … 1 We have to find the mass of the following thin bars wi...

Q: Sketch the plane curve represented by the parametric equations x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π ...

A: Given  x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π

Q: A race Runner A begins at the point s(0) = 0 and runs on a straightand level road with velocity ν(t)...

A: Given: Runner A start at the point s0=0 and run with velocity vt=2t and runner B start at point s0=8...

Q: For the function f(x) = ex , find a first-degree polynomial function               P1(x) = a0 + a1x ...

A: Given  fx=ex To find a first degree polynomial P1x=a0+a1x whose value and slope agree with the value...

Q: Objective function z = 5x + 6y with constraints x ≥ 0, y ≥ 0, 2x + y ≥ 10, x + 2y ≥ 10, x + y ≤ 10 S...

A: a. Graph the inequalities as shown below. From above graph, the coordinates of the feasible region ...

Q: find the distance between points P1 and P2. P1(-1, 1, 5), P2(2, 5, 0)

A: Given points are: P1=(-1, 1, 5) and P2=(2, 5, 0) The formula to find the distance between two point ...

Q: Expand and evaluate numerical terms: ln (e19x20)

A: Consider the given logarithm  lne19x20

Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area amo...

A: Given information: V=64 m3  

Q: Assume f (x) = 6 / x. What is the slope of the line tangent to f when x = −2?

A: Given: fx=y=6x; x=-2 we know that slopem of tangent at pointx=-2 is given by m=dydx|x=-2            ...

Q: Let lim, 1 h(x) = 5, lim, 1 p(x) = 1, and lim, 1 r(x) = 2. Name the rules in Theorem 1 that are used...

A: Given  limx→1h(x)=5,limx→1p(x)=1 and limx→1r(x)=2

Q: Find δƒ/δy as a function if ƒ(x, y) = y sin xy.

A: Given function  ƒ(x, y) = y sin xy. Partially differentiate the above function w.r.t "y" ∂f∂y=ysinxy...

Q: Solve the polynomial inequality -x2 + 2x ≥ 0and graph the solution set on a real number line. Expres...

A: Given inequality, -x2+2x≥0                 

Q: The graph of f(x) = x3_______ to the left and______ to the right.

A: Given function - f(x) = x3Let us draw the curve for the point x=-5 to x=5, by finding corresponding ...