1. Calculate the following limits (showing all working): log,(n) + 5" n-0o log7(n) + 7" Vn5 + 2 + /2n® + 1 (a) lim (b) lim 2n3 + 100 27" (n! + 500n) (c) lim n+0 33n+2(n! + n500)

Q: QI: Find dyldx for the following functions:- (3) y = (tan x)tnz+ t (4) y = sin-(x² +x) + 5"

A:

Q: sec(0) = cot(0) = (b) y (1, -1) sin(0) = cos(0) = tan(0) = csc(0) = sec(0) = cot(0) =

A:

Q: 2 3 To find the blue shaded area above, we would calculate: f(x)dx = area

A:

Q: for the N(0) is it 0k? or can I write it just k?

A: Yes, N0=-12i+12j+0k.

Q: Find V x (V x F) If F(z,y.2) 10ryj+5zyzk. V x (V x F)

A:

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 16 r(t)

A: The given plane curve is   x2+y2 =16.  We have to represent the curve by a vector valued function…

Q: Obtain the inverse transform of the following 2s-3 1. s2-9 10 (3s2+12) + (s²–25) 3s-2 3.…

A: As you have asked multiple questions so I have answered only first question as per the…

Q: Edit Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places…

A:

Q: Find the area of the reglon bounded by the graphs of the equations. y = -x+ Bx, y = 0

A:

Q: Solve the triangle. 5 B. A (Round to one decimal place as needed.)

A: On solving this we will get

Q: Evaluate sin? xcos xdx .

A: To evaluate: ∫sin2x cos3x dx=∫sin2x cos2x cos x dx=∫sin2x (1-sin2x) cos x dx

Q: xp - )s ɛ

A: As per the guidelines I can solve only first question

Q: Given x² + 13x + • 40 f(t) = 1+ cos2(x) At what value of t does the local max of f(t) occur? rp- t =

A: Here, the given function is: f(t)=∫0tx2+13x+401+cos2xdx

Q: 9. Let A be the coefficient matrix for the system of linear equations: 2x + 9y – 5z = 1, — 6х — 2у +…

A:

Q: What isfor the curve given by x = (t – 1)³ and y = vt ? | dx 1 2VE 6VE(t-1)2 3(t-1)2 O Option 4…

A: Using chain rule of differentiation

Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

A:

Q: 10 dx 5. S (10 +1)5 6. S 2r(e**+1 – 2**) dx

A:

Q: What is the radius of convergence of (п + 2)! (x+1)"? n! n=0

A:

Q: B. Find the interval of convergence of the power series and find the sum of the series as a…

A: Series convergence

Q: 2. ydx + (3x – xy + 2)dy = 0

A:

Q: dx Half-angle Substitution cos x +sin x-1

A:

Q: (E – 4)A^ = -글Vyy-3), 1sys 25 ter a fraction, integer, or exact decimal. Do not approximate.

A:

Q: your

A: Please refer to the image below

Q: this

A: We will evaluate the integral.

Q: Determine the general solutions of the following differential equations. 1. (2x - xy2 - 2y + 3)dx –…

A: We can solve 1 problem only.

Q: Perform the addition or subtraction and use the fundamental identities to simplify. There is more…

A:

Q: 3. a) Determine the slope of the function, h(x) = 4sinx at x =

A:

Q: Which identity is most useful in evaluating sin² x dx? sin? x + cos? x = 1 cos 2x x = 1- 2sin? O…

A: The given integral,         ∫sin2x dx

Q: Use Disk Method only Find the volumes of the solids generated by revolving the regions bounded by…

A:

Q: f(x) = x* - 32x + 5 (a) Find the critical numbers of f. (Enter your answers as a comma-separated…

A:

Q: x³ +x 3+X 2. Evaluate dx X O x3 + 3x + C O 2x + C -+x+C

A:

Q: If f(-x)=(2,-1), what are the coordinates of f^(x)?

A: Given that,  f-x=2,-1

Q: Determine a minimum radius of convergence of a power series solution about x 2 to (x2 + x)y" + 3y' –…

A: We can solve as follows

Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 ||M(t)||* 15: r(t) = t’i + tl5j K(t) =

A:

Q: 3 of 20 Select the best answer. (2e + 1)ª lim z+00 (tan(x))- O DNE

A: We have to find the limit.

Q: The graph of the function f (2) = 2 arcsin(x – 4) +1, is best pictured by:

A: We will put the x values and get the f(x) values.

Q: If z = 52? – 3y? + 4y, find the differential dz. You should have variables dz, dy, y, and z in your…

A:

Q: A chain saw requires 2 hours of assembly and a wood chipper 5 hours. A maximum of 30 hours of…

A: We have to find the number of chain saws X and the wood chippers Y to maximize the profit P(X,…

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A:

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 10tj – 3Vtk) dt

A:

Q: 5. Which of the following is (a) n! n=1 80 (b) n=1 (c) E T=D1 (d) -1)" (2n)! T1

A: We have to find out the power series

Q: Show that the function f defined by 1, (x, y) = (1, – 1) f (x, y) : .2 x + y (x, y) # (1, – 1) x + y…

A:

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: 11. Let -4 А -4 -4 -3 -3 (a) (i) Show that -4 is an eigenvalue of A with corresponding eigenvector…

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

Q: 6. What is the general solution of the following differential a²y.cdy d²y equation -52…

A: We need to find general solution.

Q: Find the exact value using a sum or a difference identity. SHOW ALL WORK– include the formula,…

A: cos(225°) here 225° = 180°+45° cos(225°) = cos(180°+45°) cosθ is negative in the 3rd quadrant since…

Q: Evaluate the summation S -1. 35 85 55

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = t3+3°dt f'(x) =…

A:

Q: For the curve y = f(x) = x², 0 < x < 2, its length is 2 dy` dx - {(aV17+ In (4 + v17). VI7). L 1+…

A: Apologies for the inconvenience. The correct solution is given below: Given that y=x2 Hence, dydx=2x

Q: Let y=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…

A: