Evaluate the limits. If a limit does not exist, enter "DNE". You may use a GRAPH on Desmos or plot points to see the graph. You do NOT have to do this algebraically. |x + 1| 2+1 lim z→ 1+ lim I→-1 |x + 1| x + 1 |x + 1| lim I→-1 x + 1 = =

Q: I 8. y" + siny = 0; y (0) = 1, y' (0) = 0

A:

Q: 5. Previously we used the recurrence relation dn+1 = 0.5dn + 200, d₁= 200 and the assumption that…

A: Given dn+1=0.5dn+200 and dn→L as n→∞. To find L .

Q: Find the derivative of each function. Show all your work and simplify the result completely. a un…

A: We can answer both the question as below.

Q: Find k, given f(x, y) = k(y² + xy) and [ [ f(x, y) dxdy = 54 R R=0 < x < y < 2

A: Given problem:- Find k, given f(x, y) = k(y² + xy)  And ∫∫R f(x, y) dx dy=54 where R…

Q: (c) A particle is moving such that its instantaneous speed as a function of time t (s) is given as…

A: A particle is moving such that its instantaneous speed as a function of time t s is given as…

Q: Find an equation of the line tangent to the following curve at the point (a,f(a)). f(x) = 8 ex + 5x;…

A:

Q: s ide Jan and Jim started hiking from the same location at the same time. Jan hiked at 2 mph with a…

A:

Q: In Problems 1-10, determine all the singular points of the given differential equation. 1.…

A:

Q: Without using a calculator, find the exact value of the expression: 20 cos(-315°) - 6 cot( - 135°).

A:

Q: Compute the gradient vector fields of the following functions: A. f(x, y) = 1x² +10y² Vf(x, y) =i+ j…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: If z=5x^2+y^2 and (x,y) changes from (1,2) to (1.05,2.1), compare the values of delta z and dz.

A: Given that        z=5x2+y2 changes from (1,2) to (1.05,2.1)  We have to derive value of Δz and dz .…

Q: 4. A tank contains initially 400 liters of brine holding 100 kg of salt in solution. Water…

A:

Q: A joint density function is given by (a) Find the value of the constant k. k= (b) Find the…

A:

Q: Two circles of radius 5, with centers at (-3, 0) and (3, 0), intersect as shown in the figure. Find…

A: Two circles of radius 5, with centers at (-3, 0) and (3, 0), intersect  as shown in the figure. To…

Q: Solve the problem. Find the amount of interest earned on the following deposit: $1,000 at 4%…

A:

Q: es The bearing of a ship from a lighthouse was found to be N 16° E. After the ship sailed 7.3 miles…

A: This question is based on use of Sine law.

Q: Write an expression for the polynomial of least possible degree graphed below. Leave your answ…

A: The solution is given below

Q: j dx (2x-3) 15-12x+cx 2

A:

Q: Solve the following two Euler's differential equations: (a) x²y" - 7xy' + 16y = 0 (b) x²y" + 3xy' +…

A: The given Euler's differential equations are a) x2y''-7xy'+16y=0b) x2y''+3xy'+4y=0

Q: Find the Cartesian coordinates of the given point: (r, 0) = (√3, 4). OA) (₁ (1/2, 1/³) 2 ○ (³,²) B)…

A:

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Explanation of the answer is as follows

Q: Find the limit: lim (1- cos x) sin x+0+

A:

Q: Find the length of the curve. 1 10x3' y 6 + 1 ≤ x ≤4

A:

Q: [ (x²ex - 12/²7/1₁) dx x + 1,

A:

Q: Express the following limit as an integral. lim 1-00- TL i=1 (2 (27)¹ + 3) 8-91 Ar over [1,6]

A: Note : As  per our guidelines we are supposed to answer only one question if there are multiple…

Q: Evaluate cos A. -1 COS Select the correct choice below and, if necessary, fill in the answer box to…

A:

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A:

Q: Consider the parallelepiped with adjacent edges u = 5i + 2j + k v=i+j+ 7k w = i + 9j + 5k Find the…

A: Given, u=5i+2j+k,v=i+j+7k,w=i+9j+5k.

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

A:

Q: Find the equation of the tangent plane to the given surface at the specified point. z=xsin(x+y),…

A:

Q: he indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A:

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

A: This is a problem related to vector. Please find the procedure given below.

Q: Use the information below to sketch the function. There is a horizontal asymptote at f(x)=1 The…

A:

Q: u = -7i - 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. -6 2 (b) Find the vector…

A:

Q: If $500 is invested at 4% interest, compounded annually, then after n years the investment is worth…

A: We need to find out that after 6 years what will be the invested amount become.

Q: Express in exact form: In(x² + 1)dx

A:

Q: 3 y = (₁ ² +1) ² Gi Find 13y dx²

A:

Q: Solve the equation for exact solutions in the interval [0°,360°). Use an algebraic method. 2 4 sec 0…

A:

Q: Complete the missing ones: (those highlighted ones) Integrate: .2x [cotcscdx 3 3 2x [cots (2) csc²…

A: Explanation of the answer is as follows

Q: Show that y=sec^2x and y=tan^2x have the same derivative. What can you say about y=sec^2x-cot^2x?

A: Given y=sec²x and y=tan²x Now derivative dy/dx=d/dx( sec²x) =d/dx(1+tan²x) dy/dx= 2tanx sec²x   Now…

Q: A small town in Connecticut commissioned a study to find the rate of change of its population. The…

A:

Q: Σ 4(k!) ² (2k)*! K=( a. Converges completely because re? b. diverges because r=? C. ratio test is…

A:

Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. log 6X log…

A:

Q: ct rit Find the x-value of all points where the function below has any relative extrema. Find the…

A:

Q: 1. Function f is continuous on (-00,00). Find constant k. f(x) [kx² + 2x x-kx if x ≥ 2 if x < 2

A:

Q: 1. For the following sequence, give an explicit formula for the nth term. 4 9 16 25 36 49 1' 3'9…

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: We are given the following homogenous differential equation and pair of solutions on the given…

A: Here is the solution:

Q: 2 termis U

A:

Q: IVIC Question 8 of 10 y The tangent line to the curve y=f(x) at r=1 goes ough the points (-1,3)…

A: To find out the value of f(1) and f'(1).