1. Use the Mean Value theorem to show that for any two real numbers a and b, we have | sin b - sin a ≤ b − a| .

Q: 2. Find the MacLaurin polynomial of degree 16 for the function F(x)= So sin (6xt²) dt.

A:

Q: 1. A 6 kg sign is suspended by two strings making angles with the ceiling as shown in the diagram.…

A:

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A:

Q: Solve the differential equation (1 − xy)−²dx + [y² + x²(1 — xy)−²] dy + x²(1 − xy)−²] dy = 0; y (2)…

A:

Q: 3. xy = a², y = 0, x = a, x = 2a.

A:

Q: 5) each k=1 (- series, find the sum. k - 1 6) k=1 +1) (k+2)

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Aylindrical can has a volume of 167 cm³. Use Lagrange multipliers to determine the dimensions of the…

A:

Q: 2 (2y² + 5xy 4 Ο α. χ' (y² + 2xy = y + 2) = C O b. x4 (y² O 2y + 4) dx + x (2x + 2y − 1) dy = 0 - -…

A: The given differential equation is; 2(2y2+5xy-2y+4)dx+x(2x+2y-1)dy=0.

Q: Two cars are moving towards an intersection. One car is 170 meters north of the intersection and…

A:

Q: 2. Find the domain and the critical points of the following func- tions on their domain: g(x) = 3x5…

A: Concept: Domain: Domain of the function is the set of all the inputs over which the the function has…

Q: (3x²+2x-6)dx + e²ydy=0

A: Given Problem:- 3x2+2x-6dx+e2ydy=0

Q: ㅠ 10. fž sint p cos3 p dp 2

A:

Q: Let à = = (2, 4, 5) and 6 = (3, -5, - 2). - Find the angle between the vector (in radians) Check…

A:

Q: 2. Captain Crunch wants his airplane to travel along a path that is [N60°W] with a groundspeed of…

A:

Q: (−4 − x)² +5 if x ‡ − 5 Let f(x) 4x + 25 if x = -5 Calculate the following limits. Enter "DNE" if…

A:

Q: You are driving on a toll highway from King Road to Queen Road (a 50 km drive) in 25 minutes . Two…

A: Suppose, s(t) is the position function after t hours of time in km. Now, s(t) will be continuous and…

Q: x²+1 lim x-5 √2x+2-2

A: We have to evaluate the limit.

Q: Answer the following True or False. 1 COS T dz = ln(cos z) +C

A: Our Aim is to answer whether the value of integral obtained is true or false.Given integral…

Q: The position function of an object is given by r(t) = (t2, 8t, t²- 28t). At what time is the speed a…

A:

Q: Determine the general solution of xdy + ydx = 0 A xy=c B) xy^2 = c y=c (D) X=C

A: Given Problem:- xdy+ydx=0 Find General equation  of given differential equation

Q: TU f2 sin² p cos6 p dp

A: Solution is given below:

Q: Find the arc length (s) of the curve r(t) = (est, -2e5t, 3e5t) for 0 ≤ t ≤ In (2) 8=

A: The arc length s of the curve r→t=x(t), y(t), z(t) for a≤t≤b is given by s = ∫abx'(t)2+y'(t)2+z'(t)2…

Q: 00 ΣΤΑ 1 — (−1)n-¹n² 10 Select one: O True O False ≈ 0.0676

A:

Q: TU 8. fz sin¹x cos5 x dx 2 0

A: To find the value of the given definite integral:∫0π2sin4x cos5x dxWalli's Formula:∫0π2 cosnx dx=…

Q: Consider the function f(x) = x² + 2x - 8 x - 3 a. Find the first derivative. f'(x) b. List any…

A:

Q: Use the graph of f (x): = Enter the exact answer. 1/1/00 below to find a number & such that |ƒ (x) -…

A: The objective is to find the value of delta.

Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

A:

Q: Find the unit tangent vector T(t) for r(t) = 4ti + 7t²j + 3tk. T(t) =

A:

Q: Answer: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x² +…

A:

Q: Consider the curve r(t) = (5t² − 3)i + (3t - sin(t))j. - y -5 5 a(t) = -5 5 10 15 20 (a) Find the…

A: The given curve rt=5t2-3i+3t-sintj use the derivative formulas, ddttn=ntn-1ddtsin t=cos tddtcos…

Q: Find the volume of the solid bounded by the elliptic paraboloid z = 1+ 2x² + 5y², the planes * = 5…

A:

Q: The demand for a certain product is given by the function D(q)= −2.1q+350 where q is the quantity in…

A: Given, The demand for a certain product is given by the function D(q)= −2.1q+350 where q is the…

Q: Evaluate the following limits. If needed, enter oo for ∞ and -oo for ∞, and DNE if the limit does…

A:

Q: The volume of the box is 54 cubic inches. The material for the top cost $0.08 per square inch, for…

A:

Q: = Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A:

Q: f(x) = = -2x² + 7 7x - 10 if x -1

A:

Q: What is the perimeter of an equilateral triangle inscribed in a circle with a diameter of 20 cm?

A: **As per our guidelines, we are supposed to answer only one question at a time. Since you have…

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: 9. Find the area bounded by a parabola and any right chord. (Use the parabola y² ax, chord x = x1.)

A: solution is given below..

Q: Let R be the region enclosed between the curves r²=y-1 and y=5. Sketch R and find its area.

A: The region R is enclosed between the curves x2=y-1 and y=5 we have to sketch the region R and find…

Q: Find the equation of the tangent line to the curve y = 4x cos x at the point (, - 4). The equation…

A:

Q: Find the mass of the surface lamina S of density p. S: z = √₂²x² - y², p(x, y, z) = kz ka+n 2 X

A:

Q: 0 4 From a square piece of metal of side length 6 m, four squares are removed as shown in the…

A:

Q: 2x e²x cos(y)dx + e* sin(y)dy = 0

A: This question is related to differential equations, we will solve it using given information.

Q: Find the second derivative of the vector-valued function r(t) = (4t+ 3 sin(t))i + (5t + 3 cos (t))…

A:

Q: for evey 2 adults there are 3 children if 275 ppl attend how many kids are there

A: given that, for every 2 adults,there are 3 children total number of people=275 how many kids are…

Q: 1. Which of the following relations is a function? a) {(1,9), (2, 4), (2, 3), (4, 15)} {(2, 7), (7,…

A: Recall:  A function can be defined as a relation between "each of its inputs" to "exactly one…

Q: Problem Set question: The position function for a falling objects is given by s (t) = -16t² + vot +…

A:

Q: Let the position function of a particle be r = <t, t2,0〉. Find the tangential component of the…

A: Let the position function of a particle be r=t, t2, 0.To find the tangential component of the…

Q: Differentiate the following function. You do not need to simplify the derivative. h(x) = (lnx) ³…

A: