Evaluate the definite integral. I' i+e¯*j+tk )dt O !! k 11 (ell – 1) i – (e- – 1) j + - k O ell – 1 -i - (e- - 1) j+ (e" - 1) + k 11 O ell (e-l – 1) + 11 2 O ell -i+ (e-l - 1)j+늑k 1 1 11

Q: 1. Find a power series representation of In(1+x²) and determine the radius of convergence. Eind the…

A: 1.

Q: 8. Find y'ifys34-7x+2)+4%-2

A: Differentiation

Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t?k, u(t) = 5ti + t?j…

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 9 cos(t)i + 7 sin(t)j +…

A:

Q: Determine the area of the gtven reglon. y = x + sin X Step 1 Note that for the glven reglon, x…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find r'(t). r(t) = (tan(11t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

A: r(t)=((tan-1(11t))i+tcos(t)j-tkDIfferentiate w.r.t.…

Q: Find the length of the curve z(t) = e“ cos(t), y(t) = e“ sin(t) for 0<t<7. %3D Give an exact answer,…

A:

Q: 4. A live oak tree casts a shadow 58 feet long, Find the height of the tree if the angle of…

A: Here is the solution:

Q: Evaluate the defınite integral. i+e"j+t k)dt O el2 12-( - 1) + O el2 – 1 i+ (e-' – 1) j + k el2 – 1…

A: ∫01e12ti + e-t j + t kdt=e12t12i -e-t j + t22 k01=e12112i -e-1 j + 122 k-e12012i -e-0 j + 022…

Q: 7. SavT – 1 dr 8. | (x) Væ² – 1 dx 1 dx 5x +1 9. dx 10. 3x + 9 4x – 6 dx (x – 1) (x – 2) 11.

A:

Q: Identify whether the given is a discrete or continuous variable. 1.The number of arrivals in an…

A:

Q: L x² cos 2x³ dx? After substitution is performed, which of the following is equivalent to

A: Given that the integrals  To find the evaluate and choose the correct answer

Q: Show that the function f defined by 1. (x, y) = (1, –1) f (x, y) : x² + y .2 (x, y) + (1, –1) x + Y…

A:

Q: 3. Sx³V4 + x² dx

A:

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) (1 + x)3 Σ 00 f(x) n =…

A:

Q: Evaluate the following Integrals: sin(4t) – 3 sin(2t)² dt 5 Vsech(4x) tan (4x) dx 1. 6. 7. sinh 3y…

A:

Q: C6. If FCX) =3x-4,43 li find F'(xland f"(x)

A: We need to find the first &amp; 2nd derivative of the given function

Q: The area bounded I led by y=3x and 2y=3x is revolved about the y-axis. Using circular ring method,…

A:

Q: P1: 2 cos-1 x dx 1xo

A:

Q: The equation in slope-intercept form for a line passing through the point (- 3, 2) that is parallel…

A: Topic = Coordinate geometry Correct option = A

Q: The integral of the given function f 8e2*dx is equal to а. 4(е?) b. 4(e² – e*) с. 4 (e* — е?) d.…

A:

Q: 5) Find the unit vector in the direction of v = 2i + j+k 1 - i+-j+ d) i+j+k 1 1 j+ V5 а) V5 k b)

A: We can solve this as follows:

Q: Step 1 |an + 1 an + 1 n+ 1 1, or lim = 00, then n00 an Sa, diverges. For any fixed value of x such…

A:

Q: Use the integral test to determine the convergence or divergence of the series. 1 20) E k = 1 6k- 1

A: Let's find.

Q: Solve [æ – y cot ( ) dæ + x cot () dy = 0 ; y (5) = 1

A:

Q: 1 2 3 4 f(x) f'(x) g(x) 4 1 2 3 2 4 2| 3 (x),6 2| 1 4 1 4 3 h'(4) if h(x) = f(x)•g(x) f(x) h'(4) if…

A: Our Aim is to find h'(4) with the help of table and three conditions given below:-(i)…

Q: Write the first five terms of the sequence {an}. 1 (-1)n + 11) a1 = 3, an + 1 = an

A: We can solve as follows

Q: 9x2 dx Vx3+2

A:

Q: TUTOR %3D for the function

A: The given equation is: 4x2+x3y+y2=6...(1) To find the slope, that is dydx, at Q(-1,2)

Q: .9 dx The integral of the given function is equal to 4 x-Vx a. In2 b. In3 c. In4 d. In5 e. None of…

A:

Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

A:

Q: 25. æ sec (a²) tan(æ²) dæ | sin? x dx (Hint : cos (2x) 26. 1 27. dx 4- (ӕ — 1)? 1 dx 9x² + 25 28. dx…

A:

Q: The junior class has 50 students. Fifteen students take only French, 5 students take only Latin, and…

A:

Q: X = -y A y 2Fx = 2- y² -2

A: Recall: Formula Area=∫abf(y)-g(y)dy  We have,  f(y)=2-y2, g(y)=-y

Q: The letters r and 0 represent polar coordinates. Write the given equation using r-4 cos 0 Complete…

A:

Q: dz and dy dz Suppose z is a function of x and y, and tan Vy² + x2 = 2"e®y_ Solve for

A:

Q: Find div F and curl F if F(x, y, z) = xªi – 2j + yzk. div F= curl F=

A:

Q: Find curl(5z i+ 6x j+9y k). curl(5z i+ 6x j+ 9y k) = ( i )i+(i j+( i )k

A:

Q: S V9x² + 64

A:

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 9, f'(9) = 5…

A:

Q: 7) For each set of parametric equations, eliminate the parameter and find a corresponding…

A:

Q: y x/x, x-4, and y =0 -2

A:

Q: Find the area of the shaded region. x = 2- y2 -2 2 11 A 10 - 3. 8. D. 3. 2.

A: The area of the Shaded Region: the shaded zone's area is computed by subtracting the area of a…

Q: Use Lagrange multipliers to find the point on the plane x – 2y+ 3z = 6 that is closest to the point…

A: Let, the point be (x,y,z) then the distance between (x,y,z) &amp; (0,1,4) is:…

Q: For which value of x is the function f(x) = X - 4 undefined? 2х - 8 O.4 04 1/2

A:

Q: 4) 4+ 3+ -5 -4 -3 -2 3 4 5 r -2+ -3+ -4+ 2.

A:

Q: dy 4 V -1

A:

Q: 12 Let y24xー4x+3 le) Find the eauetion.of the tangent Iine to the graph of the fuuction att x-2; O…

A: We have to find tangent line

Q: Find the limit, If it exists. x- 1 lim X---

A:

Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A: