Find the particular solution of the differential equation that satisfies the initial condition(s). f'(s) = 16s - 16s, (3) = 8 Step 1 To solve the differential equation, integrate integrate both sides with respect to Step 2 Obtain the integral on both sides. 16 16 s- 16s ds = sp ( 8s -4s + C Step 3 Substitute the value for f(3) when s 3 in the expression for the function f(s). f(3) 8 8 + C 8.= 72- + C Obtain the value of C. C =

Q: Solve the DE using Linear First Oder Method: y +yx = x - 3. if y(0) = 2 %3D

A: Solving

Q: h(x) = In|x| %D Find the derivative of the function

A: Differentiate by using quotient rule

Q: Match each series to the name used to describe it. a. geometric series b. p-series C. none of the…

A: We know that,  A geometric series is the sum of an infinite number of terms that have a constant…

Q: 2e Evaluate the integral dx 2x +3

A:

Q: Find the equation of the tangent line to the curve y = 4sec z – 8 cos z at the point 4). The…

A: We can sole this as follows:

Q: At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 22 knots and ship…

A:

Q: Use the formula k(t) = ||r'(t) × r"(t)|| to find k(t). ||r(t)||* r(t) = 8 cos(7t)i+8 sin(7t)j + 3tk…

A: Let's find.

Q: (a) Evaluate the double integral. бу 4x5 + 1 dA, D = {(x, y) |0sys 1, vỹ s xs 1} (b) Evaluate the…

A:

Q: 2. The region bounded by the given curves is rotated about the specified axis. Find the volume V of…

A:

Q: - numerical values only, do not type the units, space or comma.

A: here i am providing my handwritten solutio

Q: Use the properties of logarithms to rewrite and simplify the logarithmic expression. In In 5 In 3 In…

A: We will use logarithmic properties.

Q: Using the following vectors, determine each of the following: (Draw a labelled diagram, and give the…

A:

Q: Find the area of the region between the following curves by integrating with respect to y. If…

A:

Q: Tutorial Exercise Determine whether the series is convergent on Š1+ 10" n=1 Step 1 The series 1 +…

A: To solve the following problem

Q: 5x - 4 dx x3 + 4x2

A:

Q: (a) dz (2z4 + 1)3

A:

Q: Find the derivative of the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

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

Q: Find the 44th derivative of the function f() = cos(). The answer is function

A:

Q: Consider a closed rectangular box with a square base with side z and height y. a. Find an equation…

A:

Q: A company manufactures and sells DVD's. Here are the equations they use in connection with their…

A: Here we will find the functions,

Q: Suppose that R is the finite region bounded by y = 1, y = 1 +1, 1 = 0, and I = 3. %3D Find the exact…

A: Here R is the finite region bounded by y=x, y=x+1, x=0, and x=3.   We have to find the exact value…

Q: Find the general solution of (3xy-y²)dx-(x²-xy)dy=0

A: As the equation is homogeneous , put y=vx and solve .

Q: 10. f(x) = x² + x + %3D 1 x2

A: Derivate both side with respect to x

Q: x2+3x-1 16. Use L'Hôpital's Rule to evaluate the limit lim Write o if the limit is infinite.

A:

Q: Complete the table for the time t (in years) necessary for P dollars to triple if interest is…

A: Note that the formula for FV for compounded continouously is: A=Pert Here, given that A=3P then:…

Q: (n-2n-25n2 -80n+65)+(n-7)

A:

Q: 8. The sum below can be viewed as a right endpoint approximation for the area under the curve of…

A:

Q: In spherical coordinates equation for the paraboloid z = 2- x - y is p(cos o- psin? $) = 2 Select…

A: We have to find out  spherical coordinate

Q: 11. Use the definition of the derivative to find f'(x) for the function f(x) = x2 + x + 2. Show your…

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

Q: Use the like-bases property and exponents to solve the equation x – 6 = 23x – 1 2

A:

Q: (ii) Hence, evaluate 37x² – 17x + 38 J, (x + 6)(x – 1)²"

A:

Q: At the beginning of an experiment, a scientist has 124 grams of radioactive goo. After 270 minutes,…

A:

Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

A:

Q: (n° -9n? +16n-8)÷ (n-7)

A:

Q: Evaluate the following limits. If needed, enter oo for ∞ and -oo for – o. За3 8x? 5x | (а) lim 8 8x…

A: Solving

Q: -8x+18 f(z) 9(z) The partial fraction decomposition of can be written in the form of 8x2 + 14x + 3…

A: Here we have to solve the problem by using the concept of partial fraction to obtain the desired…

Q: dx x+

A:

Q: Find the equation which satisfies the separable differential equation dy – 15x dx with the initial…

A: Given dydx=-15xy    y(1)=-5To find solution:

Q: b) Use the velocity function v(t) = 2e" to compute the distance traveled by an object over the time…

A: The detailed solution is given below  Thank you

Q: Given the vector-valued function R(t) = -6cos(1-2t) i+8t j+6 sin(1 2t) k. Find: (a) the length of…

A:

Q: Sketch the graph of r = 6/ (3 + 3 cose).

A:

Q: 5. The continuous and differentiable function f is given by f(x) = {mx + 2 for x s-1 lx² + k_forx…

A: Here we have to find the value of m+k

Q: Find the equation for the tangent to the curve y = exp [2x] at the point (9, e 162). f(x) = exp [2x]

A:

Q: Evaluate the indicated function for f(x) = x² - 1 and g(x) = x - 3 algebraically. If possible, use a…

A:

Q: 2 (1 – :-) d.x

A: Solve the following

Q: Choose any 5 of the following problems to complete. Solve the problem by following the procedure for…

A:

Q: A rotating light is located 17 feet from a wall. The light completes one rotation every 5 seconds.…

A:

Q: Use the Root Test to determine whether the series is convergent or divergent. 1 + n- 4 Identify an…

A:

Q: dy find .2. 4 If y= 2x+ at x= 1. dx dy at x = 1 is The value of (Simplify your answer.)

A:

Q: the side length of the square pieces which are cut out. Find the value of x which gives by removing…

A: To find the value of x that gives maximum volume of box.