Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (21?) i + (5t – 3) j+ (5t²) k. t= to = 1

Q: Express à to the vector (1, 4, 2). (3, 1, – 1) as B + C, where B is parallel to the vector (1,4, 2)…

A:

Q: 2. Determine a•5 for each of the following a) å = (7, -3,5)andb = (-5,11, -2) 3. Determine the angle…

A:

Q: 2. Consider the function 2r2-9r-18 f(r) r2-r-2 (a) Sketch the curve y f(r). (b) Find the area of the…

A: Let's find.

Q: az For each of the following functions z, find and ax 3. уz + xz + ху %3 о

A: Given problem:-

Q: Solve the initial value problem for r as a vector function of t. dr Differential equation: = - 22k…

A:

Q: lo-2 2 (12y-8x) dy da

A: Given: ∫05∫0z2∫010-2z12y-8xdydxdz

Q: 2. The number, N, of bacteria in a culture at time t, in hours, is N(t) = 1000[30 + e a. What is the…

A: Topic:- exponential function  Note:- as per our guideline if more than three subparts posted than…

Q: f(x) = 8 cos Tx

A:

Q: In n Consider the series Verify that the hypotheses of the Integral Test hold, and n2 n=1 use the…

A:

Q: tan () (9) sin (4) F. Evaluate the integral r2 cos ()

A: integration

Q: 4. Evaluate the integral 2+ In? x -dx. x – x ln x (a) 3 ln |In a – 1| + 2(ln r – 1) + (In a – 1)2 +…

A:

Q: 5. The cost C (in dollars) of producing x units of a product is given by the following. C= 3Vx + 400…

A: Use derivative for finding the marginal cost .

Q: 12. A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 f/sec. Assume the…

A:

Q: 3. Which of the following is a true statementCirclc all that apply. (a) If lim an = 0, then the…

A:

Q: derivatives power series

A:

Q: Bolyng bernoulli differential equation

A:

Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

A:

Q: dz 2. Suppose z is a function of r and y and tan(VT+ y) = e**. Determine az and ду

A: Here, the given that z is a function of x and y with: tanx+y=ez2⇒z2=ln tanx+y...(1)

Q: Question * Let f be a given function. A graphical interpretation of the 3-point central difference…

A: The statement is true. see below the explanation

Q: Topic on Application of Integration - Area. Find the point/s of intersection of the graph and draw…

A: Here point of intersection of the line y=0 and y=x2-4 is put y=0 x2-4=0x2=4taking square root on…

Q: x = 2 + 5 cos t Consider the parametric equations for 0<t<r. y = 8 sin t (a) Eliminate the parameter…

A:

Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

A:

Q: 1. When do find a volume by the slic (a) A type I region rotated abou (b) A type I region rotated…

A: Given question:- When do find a volume by the slicing method? Circle all that apply.

Q: S()ム 3/2 (a²

A: Explanation of the answer is as follows

Q: An entrepreneur decided to set up a soda business. Due to this intention he bought a PET bottle…

A: 1 year = 365 days

Q: Describe the long run behavior of f(t) = 5t° – 5t% – 2t + 4 - - As t → 0, f(t) → ? v As t → 0, f(t)…

A: If degree of the polynomial f(x) is odd and leading coefficient is positive , then…

Q: x- 3 – dr x' +9.x (a)

A: find integral separately

Q: dz f1-42-223)2 3 4[3-2(2+パ) a. In 3+ JE (z+1)/ J3-2(241=+C 3-4,(2+)? 3 b. 4[3-2(2+1=)] C-A(24)?…

A:

Q: Assume Za is opposite side a, 2B is opposite side b, and Zy is opposite side c. Solve triangle ABC…

A:

Q: Find the area of the plane region bounded by the given curves: y= x, y= 2x, and x+y= 6

A: Given: y=x, y=2x and x+y=6 Now find the point of intersection between the line y=x &amp; x+y=6…

Q: For an arithmetic sequence, a17 = 2. If the common difference is 5, find: aj = the sum of the first…

A:

Q: Find the first three nonzero terms of the Maclaurin expansion of the function. f(x) = 8 cos TX ...…

A: The Maclaurin series is given by  f(x)=f(0)+f'(0)1!x+f''(0)2!x2+f'''(0)3!x3+...

Q: y = e-x" and the x – axis is revolved about the y - axis.

A:

Q: 5+ 4. 2 1+ -5 -4 /-3 -2\1 1 5 -1 -2 -3 -4 -5 + 3.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | 8 sin (x) cos°(x) dx

A:

Q: Using the fundamental theorem of calculus, find the area of the regions bounded by y= 5-x^2 and the…

A:

Q: A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a…

A: We have to check of the objects collide.

Q: Find the limit 19sin(5x) lim 28x x-0 a. 5 28 Ob. 95 28 19 О с 28 d. None of these. O e. 95 28

A:

Q: 3 Σ n(n + 1) n= 1 The first partial sum is S, = (Type an integer or decimal rounded to four decimal…

A:

Q: Find the general form of the equation of the plane containing the point Q(0, –2, 10) and the line l1…

A:

Q: a. Lim x2 + X - 2 X→1 2x2 - x – 1

A:

Q: 4. State whether the given measurements determine zero, one, or two triangles. A = 43° a = 8 b= 10…

A: We will use Sine /Cosine rule to find the triangle.

Q: sove the focowing using Lagrange Multiptiers: Maximi ze flx, Y, 2) solaject to x2 + y + 22 =1 Ax +…

A: Method of Lagrange Multipliers : 1.) Solve the system of equations .…

Q: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

A:

Q: 7. Find the price per unit p that produces the maximum profit given

A:

Q: 3. Determine the balance A for $7,000 invested at a rate of 4.5% for 20 years, compounded a. Monthly…

A:

Q: d of Variation of Parameters: [D² - 8D + 16]y = e4%sec2 %3D

A:

Q: For the following exercises, evaluate the integral. S(wew + w²ew*)dw 5.

A:

Q: ² f r' రy2 Əx? dy? dz? x² + y? + z²

A:

Q: Si cos3x cos4x dx 2 TT 6

A: