21 23 (24) EMPR Solve the differential equation by using method of un determined. coefferent; 613²116 1 (D² +16) y x+16 Sing Soline (D² + 3D +6)y=e²^s^n2x What is the par practical. Significance of general solution and particular solution. of a differential equation? Selve : (n²y = ²ny²) dn. - (n³-3n² y)dy

Q: . find f'(x) if f(x) equals the given expression. a. log (x4 + 3x2 + 1) b. log (3x2 + 2)5

A:

Q: Determine whether the improper integral diverges or converges. [.. cos(2x) dx converges diverges…

A:

Q: Find the area bounded by r = 6cos (30).

A: Given: r=6cos3θ

Q: . Given the fx²dx, which of the following is the integrand? C. x² A. 0 B. 2 D. dx

A: To determine what is integrand.

Q: Evaluate the iterated integral. [²1²₂(x² - y²) dy d dx

A:

Q: Evaluate the definite integral. √ (e19¹ ₁ + (e¹% i + e¯¹j+1 k)dt O e¹⁹ - 1 19 O el9 i-e²¹ j + ½ k 19…

A:

Q: Use the method of Laplace transforms to solve (O) 0 (0) 0.

A:

Q: Find the partial derivatives f(x,y)=e* sin(xy) of dx

A:

Q: using an online graphing app, construct three graphs which lie on the interval (-8,8) choose three…

A: The given interval is -8, 8. We have to sketch three graphs on the interval. Let us take functions…

Q: Given the vectors à, b and è in 3dD. Identify which of the following operation is possible or not…

A:

Q: y = (In x) x , find dy/dx. Oy y' = (In x)* (1 + ln x) O y' = (In x)*¹ [1 + x (ln x) (ln ln x)] O (E)…

A:

Q: Given: 6x³2x²+3 dx. Using integration by parts (udv Svdu) and dv = uv - letting u= f(x), dv= 3 g(x)…

A:

Q: Write the conjugate of √a +3

A:

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: Find the average value of the function F(x,y) = x³ex++ the region 05x≤2 and 0≤ y ≤ x². over

A: Given problem:- Find the average value of the function F(x, y) = x3 exy +(y/x)2 +(y/x)  the region 0…

Q: Find the laplace transform of f(t) = 2t¹-3e³t+10 cos 2t

A: Given that,  f(t)=2t4-3e3t+10 cos2t

Q: For the demand function q = D(p) = √363- p, find the following. a) The elasticity b) The elasticity…

A:

Q: Given s(t)=31²+12t, where s(t) is in feet and t is in seconds, find each of the following. a) v(t)…

A: The solution is given below

Q: 1. Use the graph of y = f(x) given below to find the answer to each of the following. You do not…

A: By using the graph of y=fx given below to lisy all the intervals on which f is increasing.

Q: 2. x*+5x³+20x+16 x(x²+4)² √x*+5x² dx

A: First of all, we find the partial fraction decomposition of  x4+5x3+20x+16x(x2+4)2

Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 7A…

A: Area of the Rectangle =(Length)(width). Perimeter of the Rectangle=2(length+width).

Q: Find a power series solution of the differential equation y' = 4y

A: We have to find power series solution .

Q: c. lim f(x) X→-2+ d. lim f(x) X-0

A:

Q: Use a graphing utility to construct a table of values for the function. (Round your answers to three…

A:

Q: Use the formula k(t) k(t) = ||r'(t) × r"(t)|| ||r' (t)||³ = r(t) = t²i+t³j to find k(t).

A:

Q: 16. (a) 6 dx (b) -10 (c) √² 2) |x - 2| dx (d) 17. In each part, evaluate the integral, given that…

A:

Q: 3 Find f such that f'(x) = - √x f(x) = f(1) = 12.

A: Solve for the f(x)

Q: Find the laplace transform of f(t) = 6t³ + 4t² 3 F (s) = F (s) F (s) = F (s) = F (s) F(s) = -85³ +…

A:

Q: Show that the Differential Equation is EXACT and then solve it. 2. (cos2y - 3x2y2)dx + (cos2y-…

A:

Q: 9. f(-5) = (5)²-19 = 25 -19 -6 b. lim x²-19 X→-5 = (-5)² -19 = 25-19 = 6 с C f(-5) = lim f(x) X-7-5…

A: Solution is given below:

Q: Using integration by parts, which of the following options is true of Sx arcsec x dx? Ⓒ / x ² arc A…

A: To use integration by parts for ∫x sec-1(x) dx

Q: Convert the following lines to parametric equation. a) l₁: = (1,0,1) + t(1,0,−2), t = R Z-3 b) 1₂: x…

A:

Q: a₁ = 5 9₁2=35 Find the common difference using arithmetic sequence.

A:

Q: Find an equation in rectangular coordinates for the surface represented by the spherical equation. 프…

A:

Q: Evaluate the following 1. S sin x sin (cos x) dx

A:

Q: Given sin(a)= and a is in quadrant IV and sin(B) = and /2<B<. Use sum and difference formulas to…

A:

Q: 1. y = 3x? – 2x4 - 3x3 + − − 2x + 1; y(4) - 8

A:

Q: 1. Given the following matrices: A = 1 2 3 4] 24 6 8 1 3 5 7 -1 2 -3 4 a. [(AC)BT] - DT b. [(BD)…

A:

Q: 4 3 2 +..

A:

Q: * Find the derivative lic F (+) = (+³-2+ +1) (2+²

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

Q: For each set of Polar coordinates (r, 0), match the equivalent Cartesian coordinates (z,y). Don't…

A:

Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A: Given;  Rope length =20m Height =8.2m

Q: Part 1 of 5 - Part I Given the set X = {x € R³ : d(x,a) <r}, where d is the usual metric on R³. A…

A: A set is closed iff its complement is open. So a set is not open iff its complement is not closed.

Q: 15. What is the derivative of the function: F(x) = x cos(5x) F(x) = x cos(5x) F'(x) = (x)…

A: Solving

Q: 3. For the double integral [['sin(y) dydz I (a) Sketch the region of integration. (b) Change the…

A: Given; I=∫01∫x1siny2dydx   As we know that; ∫sinxdx=-cosx+C

Q: 8. For the enclosed regions bounded by y = x² - 6x and y = -2x in the graph, what is the integral…

A: Given   From the graph intersection point

Q: Evaluate the following integrals. 2. √x* +5x³+ x+5x³+20x+16 x(x²+4)² dx

A: Solving

Q: dx √1+√√x |

A: Given,  ∫dx1+x

Q: Determine whether the improper integral diverges or converges. S™× x²e-x dx converges diverges…

A:

Q: e 3 ₁ x³ lnx dx

A: Integration by parts formula:∫u.v=u∫v-∫u'∫v