Evaluating a Limit In Exercises 13-44, evaluate the limit, using L’Hô pital's Rule if necessary. 14. lim X5- 25 –x² x - 5

Q: Find 3x? arctan x dx.

A:

Q: EVALUATION Directions: Find the derivative of the following functions. Choose the best answer from…

A:

Q: So  for the last part of the Question is it A. The Root Tests says that the series converges…

A: Apologies for the inconvenience. Here is the complete solution:   Given series is = ∑n=1∞an where…

Q: examples of geometric problems that can be solved using the parametric equations of a line and…

A:

Q: Evaluate the following integral using the method of partial fraction. (6x²+ 41x + 110)dx b. S (x +…

A: Given:     ∫6x2+41x+110x+2x2+10x+29dx Perform partial fraction decomposition:

Q: Find the directional derivative of f(x, y, z) = at P(4,5, –3) x + z _n the direction from P to Q(3,…

A:

Q: In the figure, a 2400 kg demolition ball swings from the end of a crane. The length of the swinging…

A:

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A: Solution of question is written in below steps.

Q: Find the area of the portion of the surface z=f(x,y) = x^2+ y^2 that lies below the plane z = 9.

A:

Q: '5 If f(x) dx = 8 and f(x) dx = 5.3, find f(x) dx. If f(x) dx = 31 and g(x) dx = 14, find [4f(x) +…

A: 1. ∫17f(x)dx=8 and ∫57f(x)dx=5.32.∫07f(x)dx=31 and ∫07g(x)dx=14

Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (5,…

A: x - y +2z =4 x - y +2z -4 = 0 compare with equation Ax +By +Cz +D =0 A=1 B=-1 C=2 D = -4 point…

Q: 4) The domain of f(x) = 4 cos-(3x- 1) + 5 is 3) If f(x) = 1+ x+x? then f-1(1) = a) 1 d) 2 e) non b)…

A: Since you have posted multiple questions i can do first three questions as per our company…

Q: Find the Volume y=0, y= 1/x, x=1, x=4 revolving at the x-axis

A:

Q: The graph of the derivative F'(x) of a function is given below. Justify your answers to the…

A: a. Find all the critical numbers(x-coordinates) of F(x) Answer:- at the critical numbers f'(x) = 0…

Q: Use Green's Theorem to evaluate 5x*dx +xydy where C is the triangle with vertices (0,0), (1,0),…

A:

Q: Find the area of the parallelogram that has u = 2i – j+ 2k and v = 2j + 3k as adjacent sides. %3D…

A:

Q: Evaluate * e2x sin e" dx : -e*cos(e*) + sin (e*) + c e*cos(e*) – sin (e*) + c Option 1 Option 3…

A:

Q: In dx

A: Given: I=∫lnxx2dx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: Evaluate | sin(In t) dt. t sin(In t) – t cos (In t) -t sin(In t) – t cos (In t) . . 2 2 O Option 1…

A: Substitute u=ln(t) ⟶ du/dt=1/t dt = tdu t = eu ∫ eusinudu we use integration by parts ∫fg′=fg−∫f′g f…

Q: Find the radius of convergence, R, of the series. Σ (x – 9)^ n=1 R%= Find the interval, I, of…

A:

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A:

Q: Answer the following about the function F(x)=x^4-24x^2+700. Justify all your answers. A. Find all…

A:

Q: f k车9. if D < X< 1. if 1大メ$4. if X7 4, 3-X X-3 IS the Functibn 9(x) Continuous on |I4 ? Un (-∞ 8,0)?…

A: check contineous between [1,4] g(x) = 3 - x2 between 1 to 4 check for 1+ and 1- for 1- g(x) = 3…

Q: Find the inflection points of f(x)=2x^4+19x^3−15x^2+1 (Give your answers as a comma separated list,…

A:

Q: Give the curve r=3 cos 0 a) Find the points on the given curve r = 3 cos 0 where the tangent line is…

A: θ r=3 cosθ 0 3 π4 32 π2 0 3π4 -32 π -3 5π4 -32 3π2 0 7π4 32 2π 3

Q: The vector v and its initial point are given. Find the terminal point. v = (4, -9); Initial point:…

A:

Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: A) If (xn) is a decreasing and bounded sequence. Prove that (xn) is convergent with lim xn = inf {xn…

A:

Q: Evaluate * | (0² + 1) cos 0 d0. e2sine + 20cose – sine + c 02sine – 20cos0 – sine + c Option 1…

A:

Q: Evaluate* e/x dx. x3 1 1 еx 1 ex 1 еx + с + ex + c - Option 3 Option 2 1 ex 1 еx 1 еx + с + ex + с -…

A:

Q: [x² In x dx

A:

Q: Explain why S is not a basis for M, O sis inearly dependent. O s does not span M.2 O sis linearly…

A: We can solve this as follows:

Q: e following: (x) = 2 + x – x², [a,b] = [0,3], p = 1 %3D he two conditions of the IVT are satisfied.

A:

Q: Billy savings account is currently $200 overdrawn. Billy plans on depositing $75 each week for the…

A: It is given that Billy savings account is currently $200 overdrawn and he plans on depositing $75…

Q: Choose the correct answer. 1. The sequence (x) = (-n) is. a) Cauchy b) bounded e) divergent d)…

A: We have1) The sequence (xn)=(-n) is . . . . . . . . .Now we have take n=1 x1=-1put n=2x2=(-2) So, we…

Q: (5* )csch x²+1 dy if Find dx 1. (a) y = x >0. (ecosh 5x) In Vx +1 )

A: Find your answer below

Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 11 tan ; Р(-12, 12); а—…

A:

Q: Evaluate the limit below. 36 – x2 - 6 lim 5x

A: We have to evaluate the limit                                                limx→036-x2-65x

Q: 13 dt 9+6t 4 (9+6t)5

A:

Q: Find * In(x² + 2x + 2) dx (x + 1)² In|1 + (x + 1)²| x +1 In|1 + (x + 1)2| x + 1 + 2tan-(x + 1) +c…

A: I am attaching image so that you understand each and every step.

Q: 2 sin? x 7. lim x→0 5x(1+cos x)

A:

Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

A:

Q: y" 2y'+ 17y-0; e cos(4x), e sin(4x), (-m, on). Venify that the given functions form a fundamental…

A:

Q: Write the standard basis for the vector space using x. (Enter your answers as a comma-separated…

A:

Q: Find the value of § cot³(x) cosec“ (x).

A:

Q: Consider the following higher-order differential equation. d³u d?u + - 2u = 0 dt3 dt2 Find all the…

A:

Q: 10 40 What does that mean 11 Suppose f(x)dx : f(x)dx is equal to? 10

A:

Q: ∫sec^2 x / tan x +1  dx

A:

Q: Use integration by substitution and the Fundamental Theorem to evaluate the definite integral. NOTE:…

A:

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A: