_5. Given the fox²dx, which of the following is the integrand? A. O B. 2 C. x D. dx

Q: 1. Find the equation of the plane containing the lines L1 and L2 given below: z = 4t + 3 z = -4s – 1…

A: Given :L1:  x=2t+1, y=3t+2, z=4t+3L2 : x=s+2, y=2s+4, z=-4s-1

Q: Using Linear Approximation, determine the approximate value of the following: Final answers must be…

A: Topic:- application of derivatives

Q: 3 2x hnd the f area o 2. the Sheded veg ien

A:

Q: .5 dx Vx4 – 2x2 + 1 b. 3

A:

Q: 1) Use binomial series find the power series of f (x) In(x+1)

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. You must show your work.…

A:

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 2…

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Q: In each part, evaluate the integral, given that SIx - 61, x 2 0 f(x) : x + 6, x < 0 ' %3D

A: The solution is given in the next steps.

Q: t2, -8 + 3t, g(t) = l(t -6)* + 2 cos (: -). – 6)? + 2 cos (-),

A: answer is in next step

Q: 14 y=7x-x 12 10 8 6 (6, 6) 4 y = x 2 4 6. 8. 2.

A:

Q: Find the derivative of the function at Po in the direction of A. f(x.y,z) = xy + yz + zx,…

A:

Q: Integrate sze" • fa". de Answer:

A: We have to find the integral

Q: 4. Let F = (3y cos(3z) + 4z)i+ (3+ sin(3z))j. Use the Fundamental Theorem of Line Integrals to find…

A:

Q: Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to .…

A: Given  Marginal cost = $2.50

Q: The interval of convergence of the power series x2n Σ (-3)" n=1 is:

A:

Q: Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to…

A: answer is in next step

Q: Use the Root Test to determine whether the series convergent or divergent. n2 + 1 9n2 + 8 n- 1

A:

Q: 4. Find the directional derivative of f (x, y, z) = e* cos(yz) the point (1,-2.0) in the direction…

A: I have authority to answer only one question, so  I am posting answer for 1 st question

Q: Question 2 ) Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y(0) = 3. %3D (a) Use…

A:

Q: Curve Sketching Sketch the graph of the following function: f(x) = 3x3 + 2x2 - 4x + 2

A: We have to draw the graph of given function

Q: 1 3. Let f(r, y, z) = Show that Va? + y? + z²° frz + fyy + fz: = 0.

A: answer is in next step

Q: 1. a. Show that two lines with direction vectors d, = (2,3) and d, = (6,-4) are perpendicular. %3!…

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Q: Solve the system of equations (only real solutions) by the elimination method. Check your solutions.…

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Q: Find the area A of the sector shown in each figure. (a) 72° 4 A = (b) 0.5 rad 16 A=

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Q: Graph y = - cos (x -) by Transformation of y = cosx. Show and label each Trigonometric function…

A:

Q: Evaluate the indefinite integral. for, sin( + C

A: Product Rule of integration : ∫u.v dx= u∫v dx - ∫dudx∫v dxdx .

Q: Find a formula for the nth term of the sequence. - 1, 4, - 9, 16, -25, .. Determine the sequence's…

A:

Q: . L'Hôpitaľ's Rule Evaluate the following limits or explain why they don't exist. 1 lim 1 X→0 sin x

A: Rewrite

Q: C hnd the firet order parho derivohve of 32 4 5 1. 2) %3D *y-16y²23+43x %3D h Cs, t) =° E*In ts3) +…

A: Solution is here

Q: explain

A: We will check whether fundamental theorem of calculus applies.

Q: By considering different paths of approach, show that the function below has no limit as…

A: In this question we have to find the limit.

Q: 9. Jer'y ds, C:x cos t, y sin 1, z = 1, 0<1s/2 %3D 77

A:

Q: I just want to confirm if my solution is right. Please check. If not, please correct me.

A: You have done a mistake which I have shown in step 3 of this solution. Kindly go through it.

Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

A:

Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-9)" n2 n- 1…

A:

Q: Prove the following identity: 1- tan? e cos 20 = sec e

A: solution:-cos2θ=1-tan2θsec2θ RHS=1-tan2θsec2θ        =1-sinθcosθ21cosθ2,      ∴tanθ=sinθcosθ &amp;…

Q: Find the arc length when y = 2 ln(sin ) and /3 << x < T. %3D

A:

Q: The integral (4 – y²)²dy represents the volume of a solid. Sketch the region, rectangular element,…

A: Here, the given integral is: ∫02π(4-y2)2dy which is of the form  π(outer radius)2-(inner…

Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

A: Given Data: fx=x2+ax+b

Q: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: topic- application of derivatives

Q: Select the correct answer. The graph of the function fx) = x3 defined over the interval [0, 1] on…

A:

Q: Find the arc length parameter along the given curve from the point where t=0 by evaluating the…

A: We have to find the arc length.

Q: iv. L, x* (e* – e*) dx

A: Given:

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: The Intermediate Value Theorem: If f be a continuous function over a closed interval [a, b] with its…

Q: 3 10х° -34х + 4 2x-4

A: We have to find the long  division

Q: dx Vx4 – 2x² + 1 3,

A:

Q: Question If you were to use a substitution of u = cos(x) to evaluate the definite integral below,…

A: Use the given substitution to find the new limits

Q: C Fnd the firet order parho derivohve of 4.5 f(x,4,2)= e* +y2 1.

A: We have to find the partial derivatives.   According to our guidelines we can solve only one…