Find y as a function of t if y(0) = 4, y(0) = 1. y(t): = 64y" - 144y + 81y = 0,

Q: (a) Find the derivative of f (x) = (x² + 2) (4x − 3) by first expanding the polynomials. Enter the…

A:

Q: Complete the following steps for the given​ function, interval, and value of n.   a. Sketch the…

A: Let's solve.

Q: f(x)=√x² - 6x. Use interval notation to indicate the domain of f(x). Note: When entering interval…

A: We have to find the domain of f(x) = x2-6x4.

Q: Find the solution of the differential equation that satisfies the given initial condition. x In(x) =…

A:

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" - 4y…

A:

Q: 2. Solve the DE: -+secx(y-2sec³x+2 sec² x tan x) + y cotx=0 dx

A:

Q: Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select…

A:

Q: The circle given by the equation x²+y²+ax+by+c=0 passes through the points (2.0), (-1,7) and (5,-1).…

A: Put given points into given equation

Q: 1.3 Let f(x) = Use interval notation to indicate the domain of f(x). Note: You should enter your…

A:

Q: Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 3).…

A:

Q: Evaluate the integral: -2 y√2y-y²dy

A: A detailed solution is given below

Q: Evaluate the integral: J 3 хе x³ e³x dx

A:

Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 ≤ 0 <…

A:

Q: Finals - Research All Formula in Integral Calculus.

A:

Q: Graph the function. Plot all necessary asymptotes. Plot at least 4 points. For vertical asymptotes,…

A:

Q: 1. 8. (v³ - 3y + 2)√√9+x²dx + x²dy = 0 (x² - 1)y" + 2y' — (x − 1)(x + 1)² = 0

A:

Q: (c) f(x) > 0 The solution set is (-2, 0) U (4, 00) (d) f(x) ≥ 0 The solution set is 10.01 (0,0)…

A:

Q: A company wants to start a new clothing line. The cost to se up production is 35, 000 dollars and…

A: The solution is given below

Q: Write an equation for the polynomial graphed below

A:

Q: 1 1 If g' (3) = 6 and h'(3) = 20, find f (3) for f(x) = g(x) +h(x). f(3) = (Simplify your answer.)

A: This is a problem related to differentiation. Please follow the general procedure given below.

Q: Test for symmetry with respect to each axis and to the origin. (Select all that apply.) 49 - x² The…

A:

Q: 3. Let S be the surface defined by the vector function (2e" sin v, 2e" cos v, u²+u), Find an…

A: We are given in our question a surface S defined by vector function R(u, v) = &lt;2eusinv, 2eu cosv,…

Q: nd the solution of the given initial value problem: ) = || y(4) + 2y"" + y″ + 8y′ − 12y = 12 sin(t)…

A: The solution is given below

Q: Find the average rate of change of g(x) = - 4x³5 from = - - 3 to x = 1

A:

Q: Find y as a function of t if y(0) = 7, 3/(0) = 6. y(t) = 49y" + 140y + 136y = 0,

A: The given DE is: 49y''+140y'+136y=0 So, the auxiliary equation of it is:…

Q: Evaluate the following integration.

A: Let Sinx=t

Q: Find the cosine of the angle between the vectors a = 2i +3j - 4k and b = 5i-1j+ 1k. (You should…

A: Find the cosine of angle between two vectors

Q: [²₂ 0 y√2y - y²dy

A:

Q: Use the Monotone Convergence Theorem to show that the sequence n! +∞o (1 · 3 · 5 ··· (2n − 1)) n = 1…

A: l

Q: Find the Consumer's Surplus corresponding to q=900 units. (Do no rounding of results until the very…

A:

Q: Use numerical or graphical evidence to determine the left and right hand limits of the fund |32 -…

A:

Q: 2. A right circular cylindrical container with volume 167 cm³ is to be made. Use the method of…

A: According to question,Volume of cylinder = 16π cm3

Q: n = 10, approximate the integral S Give the error of approximation for each 2 cos xdr

A:

Q: 5. Evaluate 8y Lo Lo (28+ 12 drdy (x³ 2y by reversing the order of integration.

A:

Q: It has been determined that the cost of producing x units of a certain item is 10x + 365. The demand…

A: topic - functions

Q: O A. Use the formula for the cosine of the difference of two angles to find the exact value of the…

A:

Q: in open rectangular box (no top) with volume 8 cubic meters has a square base. Express the surface…

A:

Q: What value(s) of 8 are an appropriate choice when proving the following limit? lim (10x + 4) = 44…

A: We have to solve the above problem of limit.

Q: Determine whether the series +∞0 [[CDS-¹ (-)-CO₁¹ (1) Σ|cos -1 -1 n=1 converges or diverges. If the…

A: This is a problem related to series and sum calculation. Please find the procedure given below.

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. -7t y…

A:

Q: xp (I + ²)² [ (1) 9x)x I

A:

Q: Find the equation of the tangent line to the graph of the function f(x): = x+7 x-8 at the point (0,…

A:

Q: What is the equation of the tangent line at 3x+1 0₁ = 1² of f(x) = ² 0, 2 X-2

A: The equation of tangent is :

Q: A 25-ft ladder leans against a building so that the angle between the ground and the ladder is 84°.…

A:

Q: Find the general solution of the differential equation. y (4) + 2y"+y 3+ cos(4t). NOTE: Use C₁, C2,…

A:

Q: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 0,

A:

Q: 6. Find the value of -1 I 1 = [ ²₁ [2²=2² (2² + 1²³) dy d²x + + [ ₁ [²*² (2³² + y²³) dy dz I by…

A:

Q: 1. The sum of three consecutive integers is 219. Find the integer.

A: Consider given consecutive numbers are x-1, x, x+1 Given condition, The sum of three consecutive…

Q: The graph of y=f(x) is given. Solve the inequalities. Write the solution set in interval notation if…

A: To answer the given questions using the given graph. Note that, the range of the function is:…

Q: Solve 8 sin (7x) = 7 for the four smallest positive solutions

A: