The student should answer the question below: Evaluate the given equation: | ydA where T is the region bounded above by the line y = 3, on the right by the circle (x - 4)² + y² = 9, 3 3 and on the left by the line y = -x +: 2

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ – y³, P(10,…

A:

Q: 6) dx

A:

Q: 2sinx if 2 sin x %3D what is u?

A:

Q: The percentage of P doctors who accept a new medicine is given by P(t)=100(1-e^-0.16t) Where t=time…

A:

Q: Find the area, if it is finite, of the region under the graph of y = 5x* e over [0,00). Select the…

A:

Q: x = xyln (y) – y² xy ln (x) – a² dy dx Option 3 O None of the choices dy dy dx dx x2 Option 2 Option…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) =

A: Topic = Functions

Q: The graph of the velocity function v = v(t) is given below. Determine the distance trav- eled during…

A: Distance traveled is given by area under the velocity - time graph. So, basically we have to find…

Q: Calculate the indicated Riemann sum Sz for the function f(x) = x - 9x- 22. Partition [0,6] into…

A:

Q: Let s be an acute angle and sin (s) = Find the value of cot () exactly. (Give an exact answer. Use…

A:

Q: 2. Evaluate the following limits. cos X h. lim-

A: Limit

Q: 28. f,(2,4) if f(x, y) = x* In y

A:

Q: The population of an unknown bacteria in an experimental culture is estimated by the population…

A:

Q: cOs x 1. S sin x (1 + cos x) ecosx dx

A:

Q: Use the First Derivative Test to find the location of all local extrema for the function given…

A: The given function,    f(x)=-7+20x2+10x33

Q: Let a = ci + jand b = 9i + 54j. Find c so that a and b are orthogonal. c = i

A:

Q: r = 4 cos 30

A:

Q: The equation 0-10x+5= 0 does not have a root in (0, 1) Select one True False

A:

Q: Find a1 and r for a geometric sequence {a, from the given information. 41 az = 123 and a,= 9 a1 r=

A: The given terms of the geometric sequence,a3=123 and a6=-419

Q: 2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

A:

Q: z = 3 - t , z = 6 – 4t parallel.

A:

Q: Find the slope of the tangent line to the given curve at the point corresponding to the specified…

A:

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 4/3 and whose components have…

A: use lagrange multipliers to find a vector in 3-space whose length is 43 and whose components have…

Q: Let i = (6, – 6, 1) and v = (– 5, 5, – 6). %3D Compute the following: i · i = i. i = - 6(ü - i) = (–…

A: To evaluate the given dot product of vectors u and v.

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) = %3D

A: To find the gradient of the function at the given point.fx, y=5x+2y2+4, 4, 2∇f4, 2=?

Q: The Plat circular plate has the shape af the region x+y<1. The plate including the boundary Hiw…

A: Temperature at the point (x,y) on the disk  x2+y2≤1 is given T(x,y)=x2+2y2-x

Q: Determine the intervals on which the following polynomial is entirely negative and those on which it…

A:

Q: In a certain environment, a colony of bacteria grows according to the model A = A0e^0.06t, where A…

A:

Q: a triple Integial for the solid CAclosed by X=y?+q? and xal6 Write

A:

Q: Find the derivative of the function. f(u) = u7e−u

A:

Q: Find the gradient of the function at the given point. w = x tan(y + z), (2, 15, -4) Vw(2, 15, -4) =…

A: Use gradient formula and partial derivative formula for finding the gradient.

Q: Determine where the local maxima and minima occur on the graph given. 12 10- 6- -12 -10 -8 -6 10 12…

A: Given query is to find the location of local minimum and maximum.

Q: Evaluate the sum. 7 3 ) Σ 2-3 k = 1

A:

Q: The equation x10 – 10x2+5 = 0 has a root in (0, 1) Select one:

A: The given equation is x10-10x2+5 =0  and the given interval is 0, 1. Let f(x) be continuous function…

Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

A:

Q: Find equutiuns Ofthe followicy t. 9 tangent Aane b) The nomauf line

A:

Q: (2x – 1,x < 0 a,x = 0 0. Let f(x) = x+b Find, if any, a and b such that fhas limit for all x but not…

A:

Q: Find f. f" (0) = 2e® + 3 sin 0, f(0) = 0, f' (0) = 1 Using O for 0. O f(0)=2e^O -3sin O f(0)=2e^O…

A: Given query is to find the function f(O).

Q: dy Differentiate implicitly to find dx 8x? + 9xy + 7y + 17y -8 = 0 dy %3D dx

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

Q: 5. Use L'Hospital's rule to compute the following limits (a) lim a In(x) (b) lim sin(z) (c) lim…

A: Here are the solutions: We will use L'Hospital rule and differentiate the numerator and denominator…

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) %3D Vf(4, 2) =

A: If f is a function of x and y then gradient of f is given by ∇f=∂f∂xi^+∂f∂yj^So, ∇fa,b is given by…

Q: x+2 lim sin - x+6x+8 3 2.

A:

Q: 47. Minimum material. A rectangular box with no top and two parallel partitions (see the figure)…

A:

Q: A ball is launched straight up in the air from a height of 6 feet. Its velocity (feet/second) t…

A:

Q: Evaluate the integral. -241 15 given, 7 x²dx = xdx = dx = 1. O 36 O -146 O -114 0 4 O -61

A: Given query is to find the value of the integral.

Q: Find the gradient of the function at the given point. g(x, y) = 12xe/x, (14, 0) Vg(14, 0) = %3D

A: gradient g(x,y)=(dg/dx)2+(dg/dy)2 dg/dx = 12ey/x + 12xey/xylnx dg/dy = 12ey/x (dg/dx)(14,0) = 12 +…

Q: Set up and evaluate the integral for finding the area and moments about the x- and y-axes for the…

A:

Q: Use the Comparison Test to determine if the series converges or diverges. Sn+ 6n n-1 diverges O…

A:

Q: x2 8. 36 y2 3D1 4 ニ 「て

A: This question can be solved using the concepts of standard equation of hyperbola.

Q: Give the order of the given ordinary differential equation and state the type linear or nonlinear (1…

A: Solve the following, note- your options for the degree must include 1. Because a degree of a…