Find the derivative of the function at Po in the direction of A. fxy) - - 2ху - 5у, Ро(9, - 4), А-D - 3і + 3] (DAf) (9. - 4) =U (Type an exact answer, using radicals as needed.)

Q: Use the tabular method to evaluate the integral |(x3 + 2x – 1) cos(4x)dx

A: To evaluate the following integral using tabular methodI = ∫x3+2x-1cos(4x)dx differentiable function…

Q: Use substitution to find the indefinite integral. 2 | 5z² – 3 dz -3 dz =

A: Given: I=∫z5z2-3dz   ...1   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: C. Solve as indicated. 2. Find the first 10 terms of a sequence in which the fourth term is 114 and…

A: Let us consider an A.P series with first term= a and common difference=d  Then the nth term =…

Q: Find the derivative of the function at P, in the direction of u. x- 3y g(x.y) = 2хy +3 Ро(1, - 1),…

A:

Q: Evaluate the integral: S2 (2x + 6) dx Input answer as decimal. Round off to 2 decimal places.

A:

Q: %3D Find the derivative of y = Vsinx COS I 2sin z 1. -sin z H S00 5.

A:

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

A:

Q: At low altitudes, the altitude of a skydiver and time in the air are linearly related. A skydiver…

A: Topic:   Linear Equation problem Here is the answer

Q: 1/2 dx 1-х4

A: Let 1-x4 = t

Q: Evaluate the following integral. Expand the integrand and write the resulting integral. | dx (Type…

A: Given:         ∫6x2x2+9dx   Expand the integrand.      =∫6x2·x2+6x2·9dx         =∫6x4+54x2dx

Q: the solid obtained by revolving the region bound ed by Find the volume OF about the X - axis the 2…

A: The region bounded by the x-axis, y=x2,x=0,x=2 is:

Q: In the appropriate interval of convergence, we know that x then we can deduce, by applying the…

A: To determine whether the  given statement is True or False.In the appropriate interval of…

Q: x dy + ५ ax X cost d x dy 6- -2 ५

A:

Q: Use n= 4 to approximate the value of the integral by the following methods: (a) the trapezoidal…

A: The given integral is 5/x2 limit from 1 to 4.

Q: 1-Find the area of the region R under y=x2 + 3x + 2 Between x=-1 and x=2

A:

Q: dzy and -in each of the following. Find dx2 x = x= e' cost b. y = e' sint а. y = t-1

A:

Q: || 21*y dA, R is bounded by the parabolas y = 3r* and y = 16 – r*.

A:

Q: Find (9x? - 8x + 2) dx. (9x² - 8x + 2) dx²

A: We know, ∫xndx= x(n+1)/(n+1) +C , C is a constant and for any real number n.

Q: Evaluate the integral: 2T So cos² (0)d0 *Input answer as decimal round-off to 2 decimal places

A:

Q: Show all the necessary figures and solutions to each of the following problems. 1. Find the area of…

A:

Q: Use the method of substitution to find the indefinite integral. Check your result by…

A:

Q: The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area…

A: Given that The sides Equilateral triangle are increasing at a rate of 10cm/min.

Q: Evaluate the integral 5*dx |(Type an exact answer.)

A:

Q: If y = 3 then dy/dx = 4+x O -6x/ (4 + x² )2 O 3x/ (4 + x² )² O 6x/ (4 + x² )2 O -31 (4 + x? )?

A:

Q: Q2: State and prove the first isomorphism theorem.

A:

Q: 2. Determine the value of c, so the given vectors are perpendicular: u=[-4c, 3], v = [-1, 2]

A: L

Q: If 53 + 3f(x) + 2x²(f(x))³ = 0 and f(5) = –1, find f'(5). | f'(5) =

A:

Q: Q4: Solve the following exact differential equation: 2xydx + (1 + x2)dy = 0

A:

Q: 6. the vorume formed by revolving about OY the area in the first quadrant bounded by y-4ax, y-D0,…

A:

Q: The graph of y = f(x) is given below. Evaluate | f(x)dx 6+ 3- -1 -2 -3 -4 y = f(x) -6+

A: Application of integration

Q: Cassandra has the following information about f(x) and g(x): f(æ) = x →4 - 4, lim g(x) = 6. x →4 lim…

A: This is a problem related to limit. Based on the limit properties we will answer the question. As…

Q: x-1-2 2) lim 1 1 Xー 2 2,

A:

Q: 2 x= - 5, x=2, y = 5x, y =x -6

A:

Q: 2.xy x² – y? Show that - = 0 if z= Tan

A:

Q: 2. Determine if the following integral converges or diverges. If the integral converges, find its…

A: We need to check whether the given integral converged or diverges.

Q: 4. A ball rolls horizontally off a cliff at 10 m/s. It takes 20 seconds for it to hit the ground.…

A: height = (1/2)gt2 +v0t  but here v0 = 0 for initial  height = (1/2)gt2 height = (1/2)(9.8)(20)2…

Q: The limit lim x · In cos エ→0 is an indeterminate form of type 0 ·o. Select one: O True O False

A: LetL=limx→∞ xlncos1xL=∞.ln(cos(1∞))L=∞.ln(cos(0))L=∞.ln(1))L=∞.0Which is undefine

Q: Use the tabular method to evaluate the integral fa (x³ + 2x-1) cos(4x)dx COS

A:

Q: Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 50L0ºK®1 where L is…

A:

Q: Find the critical point of the function f(x, y) —7- 5х — бх?+ 5у — 4у? This critical point is a:…

A:

Q: The flow rate of water at a pumping station on a given day, is given by the function R(t) = -t? +…

A:

Q: y = x² + 1 y = 2r- 2

A: Here, from the given figure, the area bounded by the given curves are: A=∫-12∫2x-2x2+1dy dx

Q: Consider the function: f(x) = 5x* – 2x³ + 3 Show that there is a value a e [0,2] such that f (a) =…

A: This question is based on continuity of function.

Q: lim メ→

A: This is a problem related to limit and continuity part. Please follow the procedure given below.

Q: ) Find eigennwaly gse for -5- OA= L-4 to -구

A:

Q: 1-Find the area of the region R under y=x? + 3x +2 Between x=-1 and x=2 2-the region bounded by y=.…

A:

Q: 2. y =,x = 1, x = 4, and y O is revolved about the y – axis. (Answer: 247 c. u. )

A: Given: y=4x, x=1, x=0 and y=0   The bounded region is as shown below.     Apply the cylindrical…

Q: dy =Cos x Sinx cotX 8-

A: As we know that; The standard form of the linear differential equation; dydx+Py=Q Where P & Q is…

Q: 2. Detemine if the ollowing integral converges or diverges. If the integral converges, find its…

A: Given problem:- Determine if the following integral converges or diverges. If the integral…

Q: The limit lim (x c 1 X• COS is an indeterminate form of type 0· o. Select one: True O False

A: Given: limx→∞x·cos1x   As we know that; limx→afx·gx=limx→afx·limx→agx