1 Evaluate the following definite integral. √51² (i) cos x sinx dx; (ii) [₁ xv1+r² dr. VT

Q: (a) lim (x6 + x²) X→-8 (b) lim (x6 +x7) x →∞ = (c) lim lim (x6 x7) = X→∞

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Differentiate y = ln(2e¯ª + xe y' = 0 xe¯x).

A: y=ln2e-x+xe-xd dx(lnx)=1xd dx(ex)=exd dx(a.b)=a×dbdx+b×dadx

Q: d. lim x-1 X e. lim x³ + +1 →-1 x² - 1 f. lim x→0 x→3 x - 3 6 x². 9 (x + 8) ³ - 2 X

A:

Q: 4x²-x x²-x-30 dx

A:

Q: Using separation of variables technique, solve the following differential equation with initial…

A:

Q: Which ordered pair represents the coordinates of point B?

A: There are four points A,B,C,D. We have to find coordinates for point B.

Q: Find the horizontal asymptote of the function. Give your answer as an equation of a line. If an…

A:

Q: Use a graphing utility to graph the polar equation. inner loop of r = 10 - 15 sin(0) Find the area…

A:

Q: Calculate where is the ellipse 7 fx dy + 1 6² (a> 0 and b>0) counterclockwise.

A: Given that ∮γxdy where γ is the ellipse x2a2+y2b2=1 (a>0,b>0) counterclockwise

Q: 3π (a) Write out the degree 2 Taylor polynomial T₂(x) for f(x)=sin (2x) about center a=³ 8 You may…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Given the function of f(x)= −3 + (10/7x) in the interval [−4,−1], find a point x=c between −4 and −1…

A:

Q: 1. Do the following converge or diverge? Evaluate it if it converges. Justify your claim. (i) St=10…

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly…

Q: We recall that a point P on a curve y = g(x) is called an inflection point if g continuous there and…

A: The given function is: gx=160+8x3+x4  Find the inflection point.

Q: Find u v, uu, |v||2, (u v)v, and u. (3v). u = (2, -2, 4), v = (0, 7, 4) (a) 2 (b) 24 u. V UU (c)…

A:

Q: 1. : DETAILS Find the cross product of the unit vectors. jxi Sketch your result. LARCALC11M…

A:

Q: If f(x)=5x-1, g(0)=2, g'(0)=4, and h(x)=f(g(x)), then what is h'(0)?

A: Solution:

Q: Find the volume of the solid E whose boundaries are given in rectangular coordinates. {(x, y, z)…

A: Given that z≥x2+y2z2≥x2+y2 and z≤49−x2−y2z2≤49−x2−y2x≥0,y≥0 Radius of cone and…

Q: Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem. Y(s) y" +…

A:

Q: Find the second order Taylor polynomial for f at (5,3) given by: f(x,y)=√√x + 4y - 1.

A: Please see the below picture for detailed solution.

Q: Answer 1. The position function of an object is given by s(t) = t³ - 15t² +63t, where time, t, is in…

A: We have given position of the object  st=t3-15t2+63t Velocity is given as  vt=s't=ddtst vt…

Q: 3. Find the general solution of these five constant coefficient linear homo- geneous ODES: (a) y" +…

A: General solution

Q: According to Newton's law of cooling, the rate at which an object's temperature changes is directly…

A:

Q: Find u v, uu, |v||2, (u v)v, and u. (3v). u = (2, -2, 4), v = (0,7, 4) (a) 2 (b) 24 U. V U u (c)…

A: Given :u=2,-2, 4v=0, 7, 4

Q: 2. -x+1, x≤-1 Graph f(x)=1 1-x² + 3, x>-1 in the window xmin = -3, xmax = 1, ymin = 0 ymax = 4 -3 a.…

A:

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A:

Q: Problem 4. Evaluate J. yd A where D is the region in the first quadrant that lies above the…

A: Consider the integral  ∬Dy dA

Q: For a sequence {a} satisfying Σ4" an > 0 A B C D E F A) n=1 Σ4" an B) =1 diverges. Σ6" an Σ6" an…

A: Given that , an+1an→15

Q: 4. Plot the points A = (1, -1), B = (4, 1), C = (2, 2) and D=(5, 4) and form the quadrilateral.…

A:

Q: Consumers' and Producers' Surplus The management of the Titan Tire Company has determined that the…

A:

Q: . Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = x²y + 6y²-y, subject…

A:

Q: Suppose the function f(x) has a domain of all real numbers and its derivative is shown below. f'(x)…

A:

Q: For the function below, determine each of the following. XA x - 30 (a) Find the critical values of…

A:

Q: 4) Let f(x)= et x² +1 Find the equation of the tangent line at (0,1).

A:

Q: A cylindrical soda can holds about 355 cc of liquid. In this activity, we want to find the…

A:

Q: Find the critical points of each of the following functions. Then, using appropriate technology,…

A: f(x,y)=2+x2-y2 f(x,y)=2x-x2-14y2 To find : The critical point and plot the graph to match the…

Q: Use the values in the table below to answer each of the following: x h(x) g(x) h'(x) g'(x) 0 2 1 -5…

A:

Q: Find the equation of the tangent line to the graph of f(x) = 3x - 7 at x = 0. (Use y for your…

A:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: Sequence

Q: ƒ" (1) ex+1 -1≤x≤0 = {atex = la[(x - 1)²3] 0≤x≤ 0.5' AB2: It is known that f(x) = e+4 2 where a is a…

A:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A:

Q: Calculate the median of the following data: 3-4 4-5 5-6 6-7 7-8 3 7 12 16 22 X 8-9 20 9-10 13 10-11…

A:

Q: Find the derivative of the function below. Use lower case letters. (Remember to simplify the…

A:

Q: State whether the following integral is Convergent or Divergent. 0 Lo ∞ ex dx Divergent Convergent

A:

Q: What point on the parabola y = 1 - x^2 is closest to the point (1,

A: we will find the required.

Q: Which of the following series are convergent? 1 1 1 I. 1+++. + + 2- 31 II. III. 1 1 1+-+-+ 2 3 1 1…

A:

Q: f 1-3₂² x²(x+1)(x²72)² dre

A:

Q: Determine if the following series is convergent or divergent. 5 * 4n+2 32n-1 * 21-n Σ n=0

A:

Q: For the function below, find (a) the critical numbers; (b) the open intervals where the function is…

A:

Q: Let f(u) = √u and g(x) = u = 4 + 9x². Find (f o g)'(3). (fog)'(3) = (Type an exact answer.)

A:

Q: Find the Fourier series for the following. f(t) = |2t| -π<t<π

A: We need to find the fourier Series of function f(t)= 2t on the interval -π&lt;t&lt;π