Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the unit vector u = cos ei + sin ej. f(x, y) = P(2, 0), e = - 7x + y"

Q: Use the functions below to find the given value. f(x) - 5 %3D g(x) = x3 (g f-(-5) = %3D

A:

Q: (1.5)+(-2.3)+(-0.3)+(1.2) + (1,9)? Simplify o= (a) State the answer in square root form and (b)…

A: Given query is to simplify the expression.

Q: Find the area of the region bounded by the line y = 4 - 2x and the coordinate axes.

A: Given query is to find the area bounded by the line.

Q: Let a = ci + jand b = 3i + 4j. Find c so that the angle between a and b is- Round your answers to…

A:

Q: x = In(1– y²) 0<y <½ for Determine the arc length of the curve

A:

Q: 30. | (Зи — 2)(и + 1) du

A:

Q: Eliminate the parameter on t to write the parametric function as a Cartesian equation in y = form.…

A:

Q: Evaluate e |/| 2xz dV where E = {(x, y, z) | 0 < z < 1, ¤ < y < 2x, 0 < z < z + 3y} E Round your…

A:

Q: Determine whether the lines L1 and L2 are parallel. L: x = 2 – 31, y = 4 +1, z = 7- t L2: x = 5 –…

A:

Q: k If P- q and pq=-, then p²+q² equals 2 A k/25 B 25+k c) k D) 25k

A:

Q: Find the composite functions (f • g) and (g ). What is the domain of each composite function? (Enter…

A:

Q: Find a formula for the nth term of the sequence in terms of n. 5 52 53 54 12' 15' 18' 21' 24 1 for…

A: 112,515, 5218, 5321, 5424,...Numerator:50, 51, 52, 53, 54, ....can be represented as;5n-1, for…

Q: a dx Vax - 0 Vax

A:

Q: 2

A:

Q: Evaluate the integral of· if it has an upper limit of 1 and a lower limit of 0. (x+1)®

A:

Q: Evaluate/Find the following integrals. 2 -3 dy 4. S 3 2 y +y 1 У

A:

Q: Find sin({ arccos ). (Hint: Use the half-angle formula.) 3/10 V10/10 3v10/10

A: Find the following

Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1)

A: To find the gradient of the function at the given point.

Q: Given the parametric function fill in the table. x (t) = t3 - 2t %3D y (t) = t - 3 t x -2 -1 1 2.

A:

Q: Evaluate/Find the following integrals. 8x + 13 2. S -dx- 3 4x + 8x + x + 2 2

A:

Q: What is the x-intercept of the tangent line to y=ln(x) with a slope of 8?

A:

Q: 2n Let an = 3n +5 Determine whether {an} is convergent. Determine whether an is convergent.

A: To determine whether the given sequence and series is convergent or not.

Q: Calculate the fluid force F on the shaded side of the triangular plate submerged in fluid with mass…

A:

Q: Vx-2 4. Lim x→2 Vx2-4

A:

Q: sin[arcsin(1)] = -1 1 sin 1

A: We know, sin[arcsin(x)]=x

Q: Find the 2 possible pairs of polar coordinates for the following rectangular coordinates. а) (-5, 0)…

A:

Q: Consider the following function. ix) = cot Create a table of values for the function. (Round your…

A:

Q: 2 * - 3 dy 4. S 1 y +y 2

A:

Q: Evaluate the integral of e**+1 2xdx.

A: Given: I = ∫ex2+12xdx                                  ...........1 Formula: ∫eydy = ey+C

Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1) Vw(19, 5, -1) =

A:

Q: 2 (In x dx U.

A:

Q: Find an equation of the tangent plane to the surface at the given poin h(x, y) = In Vx2 + y?, (6, 8,…

A:

Q: (a) P:4x-3y-6z - 2 0 P2: 12r +9v+ 18z-5 0 O Parallel O Perpendicular O Neither eTextbook and Media…

A:

Q: A) Write the DE that describes the model and solve it. B) Determine the time needed for the number…

A: Follow the procedure given below.

Q: VT (2x)[sin (2x²)] cos (x²) your exact-value result. Evaluate dx. Show complete pencil-and-paper…

A:

Q: If R is the region æ² + y² < 4, then Sp(æ² + y³ ) dA = S* L r² dr d0. 2

A:

Q: Let a = ci + jand b = 2i + 10j. Find c so that a and b are orthogona C = i

A: Given: a=ci+j b=2i+10j.

Q: D = {(r, y) : 1 <Ise, 0<yS In(r)}

A:

Q: Find the directional derivative of f at Pin the direction of a. f(x, y) = 4x* y²; P(3, 2); a = 3 i –…

A:

Q: Choose the values that would complete the general solution for y = arccos (-1 ±2tk HIN O O O O 0

A: Given:     y= arccos-1

Q: Simplify arctan4 + arctan (round to the nearest degree). 45° 0° 90°

A:

Q: Find the vector component of v = 2i – j+ 3k along b = i+ 2j + 2k and the vector component of v…

A: We have to find the vector component along another vector

Q: Use the root test to determine whether >a, converges, where An is as follows. n=1 332. a, = n/ e"

A:

Q: An angle's initial ray points in the 12-o'clock direction and the terminal ray rotates CCW. Let θ…

A:

Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

A:

Q: 33. (1 + r)' dr

A:

Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation and use…

A:

Q: 8) Find a power series representation and determine the interval of convergence for 2 f(x) = 3 – x

A:

Q: Find Duf at P. 3 f (x, y) = sin(7x – 5y); P(5,7); u 4 - NOTE: Enter the exact answer. Duf

A:

Q: indefinite integrals: Show complete and detailed solutions. Express your answers in simplest form…

A: