Find the average value fave of the function f on the given interval. f(x) = 4x − x2,    [0, 4]

Q: Suppose that we don't have a formula for g(x) but we know that g(2) = -4 and g'(x)=√√x² + 5 for all…

A:

Q: xp zx^x 0/ S (a)

A: The given integral is xsqrt(1-x2), limit from 0 to 1 to

Q: 2. P √√2 √2 1 2 ন and Q 1 √3 2' 2 are two points on the unit circle. If an object rotates…

A: We use the conversion from rectangular to polar coordinates to solve the given problem.

Q: 8) Find the position vector r(t) for a particle with acceleration a(t) = (5t, 5 sint, cos 6t),…

A: The acceleration a→t=5t,5sint,cos6t

Q: 46) In- A) = -2 = -2 B) e-2 = -1/2/2 e² (2²-0 = e D) -

A: NOTE: Refresh your page if you can't see any equations. .

Q: Consider the integral 9 3 1² ( 2²/2 + 5) dz dx X (a) Find the Riemann sum for this integral using…

A: Given integral  ∫59( 3x + 5 )dx

Q: Express the vector (5, 1) in terms of the standard unit vectors i and j.

A:

Q: 4. = 11, || 17, and the angle between u and V (when placed tail-to-tail) is 63°. Find the magnitude…

A:

Q: 3. f(x, y) = x² + 4xy + y²

A:

Q: A circular swimming pool has a diameter of 18 m, the sides are 3 m high, and the depth of the water…

A: Given: Diameter= 18 m Sides = 3 m  Dept = 3 m  Acceleration = 9.8 Density = 1000

Q: (c) \P) 3-X _x(x2 + 2) - dx

A:

Q: a. Show that the function is a solution of the differential equation b. Show that f(x) = e. f(x) =…

A:

Q: 五 -3-2 5+ -5+ 1 3 6 A H

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 71. an = 1 Vnt tr 1 √2n4 san s 1 √²n²

A:

Q: about the x-axis the region under the curve y = x¹/6 from 0 to 3. You first slice through the…

A:

Q: 4. Categorise (with reasons) the eigenvalues and eigenvectors of the following phase portraits. (a)

A: Given the phase daigram.

Q: The next step is to find du = g'(x) dx. First find g'(x). g(x) = x + 9x 6.x³ +9 Therefore, we have…

A: Find where wrong Your wrong 1/u it is wrong Right is 1/u^2

Q: 5. Perform the line integral [F-dr, for the vector field F(x, y) = (²²) i + (³²) j where the curve C…

A:

Q: Find the second partial derivatives of the function f(x, y) = x³y5 + 2x5y. a2f дх2 1. 2. 3. 4. - 82f…

A: The function is given by fx, y = x6y5+2x5y To determine: The expression of the following second…

Q: Find the trigonometric form of the complex number shown below. 10i

A:

Q: Tutorial Exercise Step 1 1 Use a definite integral to find the area under the curve between the…

A: We have to find the area under the curve.

Q: 1) Evaluate the indefinite integral: fsin³r cos8 x dr

A:

Q: Construct a problem where the area under the curve of a graph is equal to 2.

A:

Q: if f(x) = 19 9² (4) = 3 Where find f'(14) √x g(x), 9(4) = 2 and

A: if fx=xgx

Q: If f(x) da = 16 and ¹ Answer: fr f(x) dx = 3.1, find f(x) dx.

A: We know that the formula int_a^b f(x) dx=-int_b^a f(x) dx

Q: Example 2: Consider the graphs of the functions f(x) and g(x) given below. Find each of the…

A: a)limx→1f(fx) limx→1f(fx)=flimx→1fx ⇒f(3) =2 limx→1ffx=2

Q: = x², y = x² −2x+2 7. Let a, b be fixed real numbers. Let P₁, P2 be parabolas with equations y =…

A: Note: As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Consider the function where b is a real valued constant and b 5. Fill in the following blanks: The…

A:

Q: Determine convergence or divergence of the series. n=1 In n 4n-5 O Converges O Diverges W

A: The given series is:∑n=1∞ln n4n-5n

Q: Let the vector v have an initial point at (1, 0) and a terminal point at (4, 2). Determine the…

A:

Q: Find the direction angle of the vector. Round to the nearest hundredth of a degree for the angle. p…

A: We have to find the direction angle of the given vector. First as direction angle we will measure a…

Q: 21. f(x) = ln (5 - x)

A: 11-u = ∑n=0∞ un = 1+u+u2+u3 +...

Q: ππ|2 ff sin(2x)cos(3y)dx dy 00

A: Use the double integral separate the variable

Q: Find the area between y = 1.5x + 5 and y = x² - 2. The -2 and x = 3.5. graphs intersect at x = − -4.…

A: The equation of curves are y=1.5x+5 and y=x2-2

Q: 2. Compute the following limits x²-x-2 x 2 x²+x-6 (a) lim (b) lim xxx² (c) lim x² - 2x + 1 x-3

A:

Q: Write the vector shown on the graph below as a linear combination of standard uni vectors i and j.

A: Graph

Q: Determine whether the given point (x,y) is on the unit circle. Nin Ο No OYes QUESTION 20 Use the…

A:

Q: 03 3 Grwein (wave → ( x² - y²)³ zy <= Find 2 du - 5 dy @ (3,1) dx 2 dz.² 512 27

A: Given curve: x2-y2xy3=51227 To find 2dydx-5d2ydx2 at point 3, 1.

Q: Write the vector below in trigonometric form. m = −10i +10j m = 4√5 m = 4√√5 m = 10√/2 m = 10√/2…

A:

Q: Octo of large aquarium + Cos (7²) gallons f(t) = 100 - † (os (7²) leaks OLA of the Flows Salt Water…

A:

Q: e 흐 e

A: We have to categories the eigen values.

Q: 9) Find the arc length of r(t) = (cos 4t, sin 4t, t) from t = 0 to t = 2.

A:

Q: Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your…

A:

Q: 9. Find all the vertical and horizontal asymptotes for the following function and indi- cate the…

A:

Q: (2) g(x)) = f(z) g(z) + g(z) - f'(x). (a) For each of the following functions, use the Product Rule…

A: Note : As per our Guidelines , we can solve first part as your all parts are not small and also in…

Q: Use the limit comparison test to determine if the series converges of [ 30².6 n-o O Converges O…

A:

Q: Use Newton's method with the specified initial approximation x, to find x3, the third approximation…

A:

Q: 17. bn = 5n-1 12n +9

A:

Q: (b) So = x-4 r2 – 52 + 6 dx

A:

Q: 5) Calculate the Taylor polynomials T₂ (x) and T3 (x) centered at x = a of the function f(x) = sin x…

A: