Given the series: 1. k+3 does this series converge or diverge? diverges converges If the series converges, find the sum of the series: 1 k+3 (If the series diverges, just leave this second box blank.)

Q: sin x 3. Vcos x

A: To evaluate: I=∫0π2sin5xcos x3dx=∫0π2sin4x(cos x)13sin x dx=∫0π2(sin2x)2(cos x)13sin x dx=∫0π2(1-cos...

Q: Determine the standard form of equation of a hyperbola with foci at (-1,0), (1,0) and one of its asy...

A:

Q: Find the position function s(t) for the given acceleration function and conditions: a(t) = −2t+7, s(...

A: The acceleration function,a(t)=-2t+7, s(1)=8, v(2)=-3

Q: f(x) = 5. (a). Use f'(x) = lim (e+h)-/@) to find f'(x). %3D %3D T+3 h→0 (b). Find an equation of the...

A: Given query is to find the derivative using definition and the equation of tangent at x =2.

Q: Find the surface area generated by rotating the given curve about the y-axis. x = et - t, y = 4et/2,...

A:

Q: For the next three questions, consider the differential equation: y" – 2y' + y = e* arctan r

A: Particular Integral

Q: 1. Evaluate the following limits. x+ Vr - 3r а. lim Vr4 + 3x

A: We have to find limit

Q: 2 COS os²(5æ) sin*(5æ)dr 4

A: This is a problem of integration. Based on the general formula of integration we will solve the prob...

Q: Which graph shows the function f (z) = tan z? 2- 0. 2x -1 12 4 3 2 -1 -2 Cunpy

A: Topic:- trigonometry   

Q: Given an infinite series, discuss a strategy for deciding what convergence test to use

A: First i have written an infinite series and told about convergence test of similar series named p-te...

Q: Transform the polar equation ?r = 5 cos(0) to an equation in a and y.

A:

Q: What are the coordinates of the vertices of the hyperbola whose equation is given by 4y2 – x² = 4? A...

A: The given hyperbola equation,        4y2-x2=4

Q: ind the equation of the curve at every point of which the tangent line has a slope of -e-.

A:

Q: Find the​ curve's unit tangent vector.​ Also, find the length of the indicated portion of the curve.

A: Given that      r(t) = 6t3i + 2t3j + 3t3k  , 1<=t<=2 

Q: 4. Perform the following operations involving complex numbers: a. (2 + 7i) + (3 – 4i) b. (9 + 5i) - ...

A:

Q: Write the improper integral as a sum of limits of proper integrals. Do not attempt to evaluate the i...

A:

Q: 6. Let T: R → R be defined by T((a, b,c)) = (a, a – b,b + c). Determine whether T is a linear transf...

A: 6. T:ℝ3→ℝ3 be defined by Ta,b,c=a, a-b, b+c

Q: TRUE or FALSE 1. The co-vertices are on the hyperbola. 2. An ellipse contains its co-vertices. PL...

A:

Q: 10. Using the method of undetermined coefficients, write the form of the assumed particular solution...

A:

Q: A chemist has three different acid solutions. The first acid solution contains 25 % acid, the second...

A: We have to find quantity of each solution in liters.  

Q: 22+4x-5 Find the derivative: y = (3a2+1)4

A: Given Find derivative of y=x2+4x-53x2+14

Q: Find the slope of the tangent line to the graph x/y=cost at the point (-pi,pi

A: Find your answer below 

Q: Give the coordinates of the vertex to the right of the center in the equation: (x- 3)2 (y-1)² =1. 9....

A:

Q: $6. Determine the complementary function for the given DE.

A:

Q: Find the limit of x^x as x approaches 0 from the right.

A:

Q: dy for: (x + y) = x – y + 8 da 1. Find 2. If a ball is thrown vertically upward with a velocity of 8...

A:

Q: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 8 ft above the bo...

A: Given: A dingly is pulled toward a dack by a rope from the bow through a ring on the deck 8 it above...

Q: Find the amplitude of the graph of gy=-7cos O 18% 7. 77 O-7 07

A:

Q: Find the derivative of the following exponential functions: ans. y' = -4e-4x 1. y = e-4x ans. y' = x...

A:

Q: An object moves along the a-axis, its position at each time t > 0 is given by æ(t) = t" 3 4 +t. Dete...

A:

Q: If the relationship between Y and X is negative (as X increases Y decreases), then there are more po...

A: Here, the given relation between Y and X is negative that is as X increases Y decreases. One of the ...

Q: solve the differential equation: y2dx+(x2-xy-y2)dy = 0

A: Given:    y2dx+x2-xy-y2dy=0

Q: Study the figure below and give the value of x and y", If the least squares equation is y= 18.9476+1...

A:

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral wi...

A:

Q: Find the area under the curve – 1.5 0.5x from x = 9 to x = t and evaluate it for t = 10 t 100. Then ...

A:

Q: Let sk En(0.1)" n=1 Find s9.

A: Given that sk=∑ n=1k n (0.1)n -(i) Our Aim is to find s9=?

Q: The differential equation of the form = sin x has a degree equal to dy %3D Enter your answer as a dr...

A: We have to find out degree

Q: Find the derivative. 9. y =

A: The function is given by y = 94x34 Formula Used: ddxaxn = anxn-1 where, a is constant To evaluate: T...

Q: 4. The height h (in metres) of a certain section of a roller coaster is modelled by the equation h(x...

A:

Q: Water is poured into a conical container at the rate of 10cm³/sec. The cone points directly down, an...

A:

Q: Evaluate the improper integral if it converges, or else show that it diverges. 16 dx

A: Given query is to find the value of integral.

Q: f(2) Suppose that the limit value of: lim a , what does imply? g() O a. A limit exist. O b. The nume...

A:

Q: as, consider the different

A:

Q: Use a graph to determine whether the given function is continuous on its domain. HINT [See Example 1...

A: Given function hx=1+x2   if x≠06          if x=0To find  : point of discontinuitylimx→0+hx=limx→0+ 1...

Q: t nd the arc length parameter along the curve from the point where t= 0 by evaluating the integral s...

A:

Q: Determine the standard equation of the ellipse that satisfies the given properties: 16 3, horizontal...

A:

Q: y - 3y + 2y = 3e + 2e2 %3D

A: Given: -The ordinary differential equation is, y''-3y'+2y=3ex+2e2x To find: -The solution of the giv...

Q: Determine the solution to the second order homogeneous initial value differential equation 1 y"+ 3 y...

A: Topic:- differential equations

Q: 8. Compute the derivative of the following equation. (1) y = (x +1)3(2x – 2)2 (ii) y2-4x² y+x=16

A:

Q: -1 | tan *xdx

A: The given integral,       ∫tan-1x dx