Find the derivative of the function. HINT [See Examples 1 and 2.] 4x r(x) = 5 х0.1 + 4 6 4 5x1.1 r'(x) = %3D

Q: A geometry teacher wants to draw a rectangle inscribed in the ellipse x? + 4y² = 16. What is the are...

A:

Q: ja2x* +x-a))dx = 24, 3. If find the value of a constant.

A: Here, given that: ∫026(2x2+x-a)dx=24⇒∫02(2x2+x-a)dx=246⇒∫02(2x2+x-a)dx=4...(1)

Q: A particle moves according to a law of motion s = f(t) = t3 - 15t2 + 72t, t2 0, where t is measured ...

A: Solution

Q: For what values of a and b wou la the function f be continuous at every 'humber x'? real ax + 26 if ...

A:

Q: Find the slope of the line tangent to the graph of ye* = y2 + x – 6 at (0, 3).

A: Given query is to find the solpe of tu tangent line at indicated point.

Q: 4. Lim log1/2 x x-2 sin 2x 5. Lim

A:

Q: (3) A firms production function is Q(L) =15L -0.12', where output (Q) is a function of a single inpu...

A: The given function of production is: Q(L)=15L2-0.1L3 where L is labour (number of workers).

Q: Which of the following series convergence tests could be applied to the infinite series (2n)! E? Che...

A:

Q: The variable point (t²,t+1) lies on a parabola. (i) Sketch the parabola for -2 <t<2.

A: See the answer below

Q: Task: Find the general solutions of the following differential equations 1. 2x(y+1)dx + ydy = 0

A: 2xy+1dx+ydy=0

Q: Detrminc Partiular solurion y?dx + (x*+ 3×y+4y?) ay:0jx=2,y=1

A:

Q: 11) This is a function written in vertex form. F(x) = 2(x- 3)² + 4. %3D Describe the number of units...

A: As per the company guidelines We can first question only. Please understand. Kindly repost the quest...

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) f(x) = 5x...

A: function  fx=5x2-6x, find the critical points?

Q: y" +y = 1.

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as ...

Q: Find the unit vector ey, where v = (9,0,7). (Give your answer using component form. Express numbers ...

A:

Q: How does mL=(M+m)D simplify to m=M (D/L - D)?

A:

Q: You have been given the graphs below, which one of them represents f(x,y)=9-x²-y² ? 1) 2) 3) 4) 30 2...

A: Here we have to represent the graph of the given equation f(x,y)=9-x2-y2 ..............................

Q: Consider the following alternating series. k9 と(-1)+1 k12 + 4 k=1 a) An alternating series can be wr...

A: The given series is (-1)k+1 k9/(k12+4). 

Q: F(x, y) = (2x + y)i + (3y – x) j on a particle that travels on a plane along the straight lines from...

A:

Q: 4. (4x2 - y?)dx - xydy = 0

A: Let's find. 

Q: of at (r, s) = (1,0), where ds Use the Chain Rule to evaluate the partial derivative f(x, y) = In (x...

A: Solve by partial derivatives

Q: 13. Let M be the region under the graph of f(x) = 3 from x = 0 to x = 5. %3D A. Find the area of M. ...

A: Explained below 

Q: If yex – 6y = 5, find dy/dx. dy dx

A: We have to find the derivative of the given equation.

Q: Obtain the general solution. (xy)dx + (x² + v²)dy= 0 OC- 2(x2 + xy + y?) OC- y^(2x² + y?) OC = y(2x2...

A: Given (x.y)dx + (x² + y²)dy = 0

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer ...

A: Given two lines, x=2-t, y=3+3t, z=4+3tAnd x=5t, y=1-15t, z=4-15tThat isx-2-1=y-33=z-43=t            ...

Q: Let u = u(x, y), and let (r, 0) be polar coordinates. Then 1 || Vu||? = u; + u3 Use this to compute ...

A:

Q: Find the directional derivative of f(x, y, z) = xy + z° at the point P = (3, –2, –1) in the directio...

A:

Q: Find the intervals in which the function f(x)= 2x* +8x -5 is concave up/concave down. Also, find the...

A: inflection points of y=2x4+8x3-5

Q: 7/2 r = 6 cos 20 4 2 -4 -2 2 4 -2 -4

A:

Q: Problem 2: Show that (n + 23)³ is O(n³)

A: f(n)∈O(g(n)) iff ∃ scalars C,n0 such that f(n)≤Cg(n) ∀n≥n0

Q: If x³ + 4x³y? = x – y³, find dy/dx. 3,2 | dy %D dx

A: Here we have to find the implicit differentiation.

Q: 3. Find the Laplace transform of the piecewise function 03

A: To find the laplace transform of the given function.  

Q: Find the limsup and liminf of the following sequence: sin (2) а) аn = n

A: Here we have to find the limsup and liminf of the given sequence an .

Q: Suppose that a company's sales volume y (in thousands of units) is related to its advertising expend...

A:

Q: 22. dr

A: Please see the answer is below.

Q: This question has two parts. You may open the second part after you submit correct answers to the fi...

A: Given query is to apply ratio test.  

Q: Given the function f (x) =V=² +1, z € [0,1] (a) Enter f' (x) x*(x^2+1)^(-1/2) (b) Enter the inverse ...

A:

Q: Find the slope of the tangent to the curve y² In(x) + x<y = 5 at (1, 5).

A:

Q: ues hon ( 3): Find equation of Lie in each Case:- ) passing Hhe points 2) passing the point (2,-3) a...

A: In this question we have to find the equation of line.

Q: Find the limit. 1. lim (1.001)* 2. lim (1.001)* ズー ex -e -3x 3. lim 4. lime 3x -3x e* +e*

A: Topic = Limits As per guidelines , At a time only three sub-parts can be answered. Please repost for...

Q: A tank is full of water. Find the work required to pump the water out of the spout. Use the fact tha...

A:

Q: H.W: Evaluate the integral 3. -4y)dydx x*ydxdy 1 -1

A: ∫xndx=xn+1n+1

Q: 13–16 Show that the equation represents a sphere, and find its center and radius. 13. х2 + у? + z? —...

A:

Q: y(x) =x' (2x – r²)

A:

Q: Use the power reducing formulas to rewrite sin*(2x) without exponents. sin (2x)

A: Given sin⁴(2x)

Q: Use the Integral Test to determine the convergence or divergence of the p-series. 1 n8 n = 1 Σ 1 dx ...

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Suppose that a particle moves along a line with position function s(t) =2t^2 +3t+1 where s is in met...

A:

Q: Solve the initial value problem. ds 12t(31 - 1)°, s(1) =7 dt The solution is s = S.

A:

Q: Consider the equation below. f(x) = 5 cos2(x) – 10 sin(x), OsxS 2n (c) Find the inflection points. (...

A: f(x)=5cos2(x)-10sin(x)Differentiate f'(x)=10cos(x).(-sin(x))-10cos(x)f'(x)=-10cos(x)(1+sin(x))Differ...

Q: Compute the value of the improper integral. (If the integral diverges to o, type 00; if the integral...

A: Integral Test : Suppose f(x) is continuous , positive and decreasing function on the interval [k,∞) ...