14. Find X(s), given x" + 16x = t, x(0) = 0, x'(0) = 0.

Q: 2(- 1)"- n²+ 4 n – 1 n=1 n²+3

A:

Q: dy Differentiate parametrically to find dx in terms of t: x = 4t?,y= 2t3

A:

Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

Q: Evaluate the following limits: (1) lim (V +1- V). x→+∞ |2² – 1| (z^ – 1+8^) (ii) lim x-1 x – 1 x<1

A: Limits

Q: In the last 4 line, where is the ^2 in the ln part?

A: The given integral,      ∫13arctanx dx

Q: Differential Equation Classify the following differential equations.  - DEPENDENT VARIABLE -…

A: We have to classify the given differential equations.

Q: 44 3) y" +y = sec?x (Use variation of parameter method)

A: To solve the given differential equation.

Q: The graphs of the first and second derivatives of a function y = f(x) are given below. According to…

A: The graph of the first and second derivative of the function y = fx is The statement is f is…

Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

A:

Q: Differentiate exp(sec(x^2)

A: Given query is to find the derivative of the expression.

Q: The series 2" (n!)2 n=1 is divergent. Select one: True False

A: The given series is a 2n/(n!) 2. Repost the next question.

Q: A bacteria culture starts with 1,200 bacteria. Two hours later there are 1,920 bacteria. Find an…

A: A bacteria culture starts with 1,200 bacteria. Two hours later there are 1,920 bacteria. To find an…

Q: of limx¬∞ 6x²+5 x²+3x+7

A:

Q: What are intervals of concavity of the function f(x) = 2x - 6x² – 3 ? Concave upward on (1, o) and…

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Q: Find the sum of the first 7 terms of the following series, to the nearest integer. 6, 12/5, 24/25,

A:

Q: A garden lot is bounded by the curves y = x and y = 9. If its area is in square meters and it will…

A: We will find the area and cost.

Q: Give the range of the function f(x) = -x 2. all reals y ≤ 0 y ≥ 0

A: The given function is: f(x)=-x2

Q: Use the Chain Rule to find dw/dt. w = xey/z,    x = t5,    y = 1 − t,    z = 3 + 7t

A: To find out dw/dt.

Q: dy Differentiate parametrically to find dx in terms of t: 1 y = 2t2 + 4 X = |

A: x = 1/(t-1) y = 2t2 + 4 We have to find dy/dx

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 12 –…

A:

Q: 20 The slope of the function ƒ(x) = 5x - 5 is ______. 1 -5 5 -1

A:

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

A: Solution is here

Q: The graph of the derivative y = f'(x) of f(x) is given below. According to the graph, we have f(0) >…

A: We have to tell whether it is true or false

Q: Question 3. Motion with Gravity: su Neglecting air resistance, the motion of an object moving…

A: Let's find.

Q: For the following function, find its inverse. f(x)= In(6x 2)

A: Given, f(x)=ln(6x-2)

Q: Compute the given integral. fain' sin" x cos xdx +C

A:

Q: A graph of y = f (x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: Graph of the function is given, we have to find its derivative graph

Q: The velocity of an object moving along a line is given by v = 3t2 + 1 ft/s on the interval 0sts4. a.…

A:

Q: 6. Solve the differential equation: 2xydx + (x² - 1)dy = 0 А. ху - 1- с B. x'y - y = C С. x y = C D.…

A: We have to solve the equation

Q: e definite integral o5 tan(x)dr using strips of width for the trapezium rule correct to three…

A:

Q: a) ): Explam why the following series Σ (-1)"-1 1+ n3 n=1 is Alternating. b) Use the Alternating…

A:

Q: 3. Evaluate: lim -) X-0 sinx

A:

Q: BE-8- 1 (a) [. . | Determine if the vectors 0 and 1 span R° 3 (b;. | Can these three vectors form a…

A: (a)Her,e the matrix generated by the vectors is: 1000512-23

Q: A quadratic polynomial y = 4x +7x-3 has roots pand q. Find a quadratic g(x) +ar+B with roots r= and…

A:

Q: Question 19 Evaluate the integral given. c(2x)tan(2a)dx +C %3D > Next Question

A: To find out the integration.

Q: Consider the contour represented in the following figure. The points marked on the figure are А(5,…

A:

Q: Q2: A- Find the complete solution of the differential equation y"+2y'+4y cosx subjectcd to the…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point.…

A: Given: x=5 km θ=π5 raddθdt=0.3 rad/min The person and the hot air balloon form a right triangle,…

Q: The polar coordinates of a point are given. Plot the point. 57 T/2 T/2 3 2 2 -3 -2 -1 1 2 3 -3 -2 -1…

A:

Q: The series 1 Σ 2 (-1) "-1. 00 n=1 1.8 is absolutely convergent. Select one: O True O False

A:

Q: Evaluate the following integrals. Use only the variables "u" (and "v" if applicable) in your…

A:

Q: A rotating light is located 19 feet from a wall. The light completes one rotation every 5 seconds.…

A:

Q: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

A: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

Q: In what quadrant does the angle lie? 71/3 O IV II O II

A:

Q: Let i denote the square root of-1. For the two complex numbers =3e and w= 6e find 2, w. Grve your…

A:

Q: Question 2 Construction Problem A farmer has 180 ft. of fencing to be used in the construction of…

A:

Q: 19 Four different roads from Town A to Town B, and three different roads run from Town B to Town C.…

A: We will Break this question into two parts.

Q: C. Find the derivative of each of the following functions using Differentiations Rule/Chain Rule. 1.…

A:

Q: Differentiate f (x) = 7 (2-60+3). A. f' (2) = a2-6x- 3 B. f' (x) = In(7)(2x–6)7™(=²-6z+3) x2-6x+3…

A: Differentiate f(x)

Q: Express the following sums using sigma notation. c. 12 + 22 + 32 + 4² 4 c. 12 + 22 + 32 + 4? = E k=…

A: