QUESTION 3. a) Find the general solution of y" - 2 --= 0

Q: Let u= and v=. If uX v= then determine the value of 3A+B+C. Answer:

A:

Q: Given the function g(x) = 6x° + 72r² + 270z, find the first derivative, g' (1). gʻ(x) = Notice that…

A: g'x = derivative of gx with respect to x g''x = derivative of g'x with respect to x if at  point…

Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). 3 r(t) = 4 cos(7t)i+ 4 sin(7t)j + 3tk…

A:

Q: Find the marginal profit function if cost and revenue are given by C(x) = 184 +0.3x and R(x) =…

A: This is a problem of differentiation . Based on the formula and concept we will answer the question.

Q: Evaluate the definite integral. NOTE: Enter the exact answer. |ti + t*|dt (25;² + 1) – 1 3j2

A: The given integral,                        ∫05ti+t2jdt

Q: Using Disk Method solution, R is bounded by x-axis, y-axis and the line 2x + 3y = 1. This is…

A: This is a problem of finding volume using integration . Based on the formula and concept we will…

Q: Find the total area of the shaded region. 1.5- 1- (9,1) x= 9y? 0.5- 0. 4.5 13.5 6.

A:

Q: d) Classify the differential equation as separable, exact, homogeneous, or Bernoulli. The equation…

A:

Q: Find an equation of the tangent line to the graph of y = x^3 − 1 at the point where x = 2.

A: To find the equation of the tangent line at x=2.

Q: 3. Find the absolute maximum value of the function f(x)=- 1+x2

A:

Q: Which of the following is not used to determine the slope of a function algebraically? slope of…

A:

Q: Find the equation of the tangent line (s) to the following set of parametric equations at the given…

A: Given parametric equations of a curve.

Q: B) Find for the Implicit function: dy dx x² – sin(xy) + y? = 5xy

A:

Q: Solve for the indicated higher-order partial derivatives, fæx, fæy, fyy- · f(x, y) = Vx² + y?

A:

Q: What is the largest value of x for which the series (x – 11)" - n°5" n=1 is absolutely convergent?

A: This is a problem of series and sum calculation. Based on the formula and concept we will answer the…

Q: Use the Laplace transform to solve the given initial-value problem. 2y" + 3y" — Зу' - 2у %3D е",…

A:

Q: is said to be the Laplace transform of f, provided that the integral converges. to find L{f(t)}.…

A: Let's find.

Q: a) Find the linear approximation of f(x) = Vx b) Use it to approximate V26.9 at x= 27 %3D

A:

Q: Find the general solution of the following nonlinear first order ariable separable O.D.E.: x?dy +…

A:

Q: dy + 3x2 + 2y3 = 0 dx e) Solve (6x + 1)y?

A:

Q: Find the length of the spiraling polar curve 2e 40 From 0 to 27. The length is

A:

Q: f (x) = (100° + Sin (–72)) 5- Calculate the derivative: -15

A: Given function  f(x)= ( 100x5 + sin(-7x))-15

Q: Is the following statement true or false? If f(x) > 0 and g(x) > 0 and f (x) > g(x) on [a, b], then…

A:

Q: A pole that is 3653 feet long is leaning against a brick wall. The bottom of the pole is getting…

A:

Q: Given below is the augmented matrix of a system of linear equations.

A:

Q: Differentiate the following functions: i. v = 15/7(12/7+ 3t) (2x – 9) f(x) = x + 4 ii. iii. y =…

A: We can solve this as follows:

Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t< v2 In 5 NOTE: Enter the exact…

A: Let's find.

Q: Let f be a function defined for t 2 0. Then the integral L{f(t)} = e-stf(t) dt is said to be the…

A: Given problem:-

Q: 4 dx 16 + x² 2 dx X/x² – 4 2

A:

Q: Determine the value of c for which 42 8n lim (1+ n00 cn

A:

Q: Find the slope of the tangent line to the graph of y = √x − 1 at the point (5,2).

A:

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x0 sin 2x x2-16 2. lim r14 (Yx+5)-3

A:

Q: 12. S,(s² – 1) sds 13. (1² - t) dt

A:

Q: quation and reduction to linear ec

A:

Q: APPLICATION I. Find the antiderivatives of the following functions using the substituion rule. Write…

A: Solving the problem by finding the value of the integrals.   NOTE :: As per our Expert guidelines we…

Q: Find the value of (5a² – 6)da

A: This is a problem of integration. Based on the formula and concept we will answer the question.

Q: 1 Suppose that L is a location function of an object, given as L(t) : We 2t – 3 will compute the…

A:

Q: A piece of cardboard measuring 11 inches by 9 inches is formed into an open-top box by cutting…

A: A piece of cardboard measuring 11 inches by 9 inches.

Q: r1(t) = 3ti + 3tj + t°k, r2(t) = t'k d [ri(t) r2(t)] = dt

A:

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx2 + 5 at x=2? %3D

A: To find the tangent equation for the given function.

Q: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let  I be the 4×4  identity matrix I=1000010000100001

Q: Use De Moivre's theorem to solve for z given z = 3 – 2i. Write your answers in rectangular form. Use…

A: Given: z5 = 3-2iz   = 3-2i15                                     1-------------------De-Moivre's…

Q: 7 5 5. sec '(In t) tan° (In t) dt t

A:

Q: Find the partial derivative of the function g(r,0) = r cos 0 + r sin 0.

A:

Q: Given that u= and v= and that u.v= 199 determine the value of the constant A. Answer:

A:

Q: Let C be the parametric curve defined by                         x(t) = t2 - 2;…

A:

Q: Find an equation for a parabola with focus (– 10, 7) and directrix x = - 6

A: Find the equations for a parabola with focus (-10,7) and directrix x=-6.     Here i attached the…

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (3t + 4)i + tj, 0 <t<1

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: 2x + 6 Consider the function f(x) = . For this function there are two important intervals: (– ∞, A)…

A: