||r(t) x r"(t)|| ||r'(t)||* Use the formula k(t) to find k(t). 13 r(t) = 10 cos(7t)i+ 10 sin(7t)j+ 3tk K(t) =

Q: Find the area of the region bounded by y = 34(x + 2), x = 2 and the x-axis. %3D Answer:

A: Given query is to find the area under the curve.

Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

A: We want to find the absolute extremum of the given function on the interval [-2,2]

Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: Evaluate the definite Integral by the limit definition. Step 1 To find the definite Integral dx by…

A:

Q: (425 + 62?)dx Find -2

A:

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

A:

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

A:

Q: 1. Rules of LDef nite Integrals: 12 a) b) rpx 12 12 f(x)dr 4, find the If f(z)dr = 12, " $(z)dz = 6…

A:

Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: Evaluate the following algebraically. csc? x lim 1 O 1 O -1 8. 8.

A:

Q: Solve the following problems. 2. 2x°cos 5y+ x tan5y dy=0

A:

Q: sid problem: |-Int in 200 =lin %3D

A:

Q: dx 5-x?

A: We will solve the integral.

Q: (1) fx sin x dx

A:

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

A: Yes, N0=-12i+12j+0k.

Q: 10) Eind the eçuation of the plane Contaihins the two vectors 2and ,and the point PU2ー)

A:

Q: Approximate the area under the curve graphe

A: answer is in next step

Q: 7) Convert the coordinate (213,2) to point in' polar Coordinates. polar coordinetes.

A:

Q: Q2: Solve the following integrals:- (1) fx² sin x dx (2) f dx 4x2- xp: (3)f x sin(x + 1)dx

A:

Q: S2 2 sin?x cos5x dx =?

A:

Q: Use the fourth Taylor polynomial for f(x) = Va at a = 9 to estimate v10. Round your answer to four…

A:

Q: 1. 3 de

A: Given integral,         ∫3 dx

Q: x2 + 2x – 1 1 True or False: lim x – 9 4 O True False

A:

Q: Which of the following systems of linear equations has a solution of (-2,-8)? S 8x + 2y = –32 | y =…

A: To determine which of the following systems of linear equations has asolution of -2, -8.1…

Q: C. Find the general solution of the given variable separable equation. 1. 2cosx cosy dx - 3Isin x…

A:

Q: Find the general solution of the differential equation and check the result by differentiation. dy =…

A:

Q: (3t – 1)66 dt

A:

Q: 7. Given that tan (A) = - and angle A is in 3rd quadrant and cos(B) = - and 13 angle B is in 2th…

A:

Q: The Intermediate Value Theorem can be used to prove that the equation x2 – x – 6 = 0 has at least…

A:

Q: Find the limit. Show all work. Vx+5 -3 1. lim X- 4

A: We have to find the limit of given 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: x +1 Evaluate the given limit of lim if it exists. 2→-1 x4 – 1 O limit does not exist 4 O -1

A: We have to find the limit

Q: Find div F and curl F if F(x,y, z) = 9e*Y i – 8 cos yj+ 4 sin? z k. %3D div F= curl F=

A: F(x,y,z)=9e^(xy)i-8cosyj+4sin^2zk ∇F=∂F(x,y,z)∂xi+∂F(x,y,z)∂yj+∂F(x,y,z)∂zk…

Q: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

A:

Q: 4. Water is draining from a cylindrical tank at 2.52 L/sec. Assume that the water tank has a…

A: Given: Water is draining at a rate of  2.52L/sec=2520 cm3/sec The water tank has a diameter of 50…

Q: Find the exact values of the six trigonometric functions of each angle 0. (a) y (-V7, -1) sin(0) =…

A: (a) From the given figure: Here, OA=AB2+OB2=7+1=8=22

Q: Find the slope of the tangent line to the parametric equations: x = 3t2 - 3, y = 2t + 1 at t = 1. %D…

A:

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

A:

Q: cos(26)= 0.647 Convergent Therefore, the sum of the series is the following. (If the quantity…

A:

Q: dy tay +x?

A:

Q: 13 1 dx 13 – x

A:

Q: Q2) Find the integral of: f*,6 tan*x dx

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i + 11 sin(t)j +…

A: Let's find.

Q: Use cylindrical coordinates to evaluate the triple integral /|I x² + y? dV, where E is the solid…

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of • sin ( z) h(x) = |.…

A:

Q: Evaluate the definite integral 6 sin(x)dx

A:

Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

A:

Q: (-5 S + (0.9)" | lim

A: Given query is to find the value of the indicated expression.

Q: Find two positive numbers that satisfy the glven requirements. The second number Is the redlprocal…

A:

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: