Let F(x) = = (x − 3)³ − 4 cos (x-3) Find lim F(x). x 3 + lim F(x) = x+3+ x < 3 3 ≤ x

Q: 4. If f is a coordinate system on a line /, determine whether or not each of the following functions…

A: We need to determine whether each will be a coordinate system or not.

Q: Alice is staying in a cottage along a beautiful and straight shoreline. A point on the shoreline is…

A: We have to find minimum time in hours.

Q: se the Second Derivative Test to find the location of all local extrema in the interval (-9, 1) for…

A: Given: f(x)=x+12x+9

Q: Using Taylor Series, what is the value of yo(4) if y'=x+y² for y(0)=1?

A:

Q: If the first 5 terms of a geometric sequence are {12, 6, 3, the formula for the nth term in the…

A:

Q: Work problem 1 Consider the ellipsoid given by the equation: .8 53 - 5z². X + y 4 8 a) i ]Find the…

A: Let's find equation of tangent plane and normal line.

Q: Find the height of the tower using the information given in the illustration. 85.829° 130 A

A:

Q: Work Problems ( your works 1) Let F(t)=(4t — t²)i+t² j+sin(5t — 10) k - - - You need to show all a)…

A: Given: Ft=4t-t2 i+t2 j+ sin5t-10 k

Q: If f is differentiable and ƒ'(x)=x³− 2x² − x+2, then f is increasing on Selected Answers: [None…

A: In this question we have to find interval in which function is increasing.

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01² - 3x +229, where a…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

Q: Discuss the continuity of the function. sin(z) ex + ey f(x, y, z) = continuous except at (0, 0, 0)…

A:

Q: Use the given acceleration function and initial conditions to find the position at time t = 1. a(t)…

A: (9)

Q: r a given cylindrical tank, the radius is 2m and the height is 18m. The tank is filled pa depth of…

A: We are asked to find work to pump all of the water.

Q: Find the unit tangent vector to the curve given below at the specified point. r(t) = 7ti−2t²j¸ t = 4…

A:

Q: Population of a certain country is growing exponentially at a rate of 1.5% per year. How long will…

A:

Q: Find the principle unit normal vector to the curve given below at the specified point. r(t) = ti+…

A:

Q: For the function f(x) = sin² x, find the absolute maximum value M and the absolute minimum value m…

A:

Q: The rate of change of N is proportional to 20 + N(x), where N < −25. If N (0) = 10, and N(2) = 25,…

A:

Q: Solve the following triangle. B = 70°, C = 50°, b = 8 O A (Simplify your answer.) a≈ (Type an…

A: We will use law of sines to solve this question.

Q: 6. Use the definition of Maclaurin series to find the first four nonzero terms of the Maclaurin…

A:

Q: tan² (x) sec¹(x) dx.

A: Given, ∫tan2(x)sec4(x)dx

Q: An annular cylinder has an inside radius of r and an outside radius of r2 (see figure). Its moment…

A:

Q: Integrate I -dz Select one: O A In 1-¹-2²+√1 − x² + C I OB. 21n1-¹³+√1 − x² + C | OC. In 1-²+√1 = z²…

A:

Q: Integrate the given function (Handwritten) tan2x + 2x^2x

A: Here we use basic formula of integration .

Q: y(y² + 1)dx + x(y² − 1)dy = 0

A:

Q: -(4x³y - 16)dy = (6x²y² – 10)dx. A) Show that the differential equation is exact. B) Solve the…

A:

Q: L 2x²³ + 8x doc 3 √x² + 4

A: This question can be solved using the concept of integration by substitution.

Q: Use synthetic division to show that the number given to the right of the equation is a solution of…

A: Given :

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations.…

A: We have to find area of given region.

Q: Integrate da - z Select one: O A. In | ¹²² | + √1 - ² + C --- I OB. 2in1 - 2in1-¹² + √1-x² + C OC.…

A:

Q: Use the triangle shown on the right and the given information to solve the triangle. b=4, A=70°;…

A: Given b=4, A=700, a=? c=? B?

Q: 1 SSR (x+y)² dxdy

A:

Q: 4. Graph this piecewise function: f(x): = x+1 -2x-3 x<-2 xM-2

A: We need to graph the given functionf(x)=x+1x&lt;-2-2x-3x≥-2

Q: 25. If f(5) = 2, then f-¹(2) =

A:

Q: Find the solution of the given initial value problem 150y" + 25y"+y′ = 0, y(0) = −14, y′(0) = 10,…

A:

Q: Determine the continuity of the function f(x, y, z)= O continuous except at (0,5, 0) O continuous…

A: topic- continuity of a function

Q: Find the coordinates of the center, foci, vertices, and the equations of the asymptotes of the conic…

A:

Q: 8. Solve the differential equation: y' √x 7y

A:

Q: The angle of elevation of the Sun is 35.3° at the instant the shadow cast by an obelisk is 741 feet…

A: The given angle of elevation of the Sun is 35.3° at the instant the shadowcast by an obelisk is 741…

Q: Choose all critical points of the function f whose gradient vector is Vf(x, y)= ○ (0, 2) O None of…

A: We have to choose correct option for all critical points.

Q: 1. Find the domain of the vector function r(t) =< ln(t + 2), t 1 - 12 21 √12 - 4

A:

Q: Evaluate the following integral using the Fundamental Theorem of Calculus. Discuss whether your…

A: We need to choose correct option.

Q: The integral is improper. Select one: True O False 2 [₁² 2x -3 x² - 9 - dx

A:

Q: Apply the Mean Value Theorem tof on the indicated interval. Find all values of c in the interval [a,…

A:

Q: 2. For Luce Landscaping, the total revenue and the total cost for yard maintenance of a homes are…

A:

Q: Use the Ratio Test to determine whether the series is convergent or divergent. 157 (n + 1)62n + n =…

A:

Q: Find the Taylor or McLaurin series for the following functions f(x) = X 4+x², a=0

A: Here , we have to find out the Taylor series expansion for the given function.    Where , given…

Q: Find all values of x and y such that fx(x, y) = 0 and f(x, y) = 0 simultaneously. f(x, y) = x² + 5xy…

A:

Q: The straight line beams between the radar dish and the drone registers a distance of 32 km. What is…

A: Given: the triangle ABC in which there is 90 degree angle at A      Use: sin(θ)=…