Find the vector of length v7 in the direction of AB + AC

Q: explain

A: We will check if the fundamental theorem of Calculus is applicable.

Q: Find all the local maxima, local minima, and saddle points of the function. 4x² + 4y² - 32x f(x.y) =…

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Q: b.

A: answer is in next step

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y.z) = xy+yz+ zx, Po(-1,1,2).…

A: Given :f(x,y,z)=xy+yz+zx

Q: lim X- Sin X X3

A:

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A: answer is in next step

Q: nt Use the model A Pe" or A P where A is the future value of P dollars invested at interest %3D…

A: Let's find.

Q: Q-2. Determine the values of x for which the function J (X) =$in Xcan be replaced by the Taylor 3…

A: We have to find the value of x as per given conditions.

Q: dx Vx4 – 2x² + 1 3,

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Q: The function x2 f(x) = 1 - x has a local maximum when x = 2. Select one:

A: We will check if the given statement is correct.

Q: x²+3 Suppose y = and x = sin (u)ln (u) a. Determine dy using the first principles definition of a…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: ley'z ds, Cis the line segment from (3, 1, 2) to (1, 2, 5)

A: Given ∫c y2z ds Where c is the line segment from (3,1,2) to (1,2,5) Parameterize the line  r(t) =…

Q: (e) If p = tą+3ī , then p, q, andr must be coplanar F Ccould be wltihear)

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Q: Find the producers' surplus at a price level of p= $57 for the price-supply equation below. p= S(x)…

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Q: iv. L, x* (e* – e*) dx

A: Given:

Q: a. f(x) = ln 3sqrt(2x^3+5) (Use log properties to simplify first)

A: Solve the following

Q: Find a formula for the general term an of the sequence assuming the pattern of the 4 16 64 256 1024…

A: we have to find out the nth term

Q: Vhich of the following are possible f '(x) for a function f(x) that is decreasing for every x > 5?…

A: We are asked to find which is decreasing

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

A:

Q: The power series representation of 1 f (x) = 5x +4 is: O 5 25 125 x+... 256 4 16 64 25 125 x++...…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: This question can be solved using the concept of unit tangent vector and length of vector curve.

Q: Find the area of the triangle having vertices at (−2,3,1),(1,2,3) and (3,−1,2)

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Q: 3. If a = 2 i-3 j+5k and b = -3 i+6k, determine a simplified vector for each of the following in the…

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: We need to evaluate :

Q: A deli sells 720 sandwiches per day at a price of $6 each. ... A market survey shows that for every…

A: Let price reduce x times Price of deli = 6 - 0.1x Number of deli sells = 720 + 20x   Revenue

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

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

Q: A company manufactures mountain bikes. The research department produced the marginal cost function…

A: Increase in cost can be calculated by finding the definite integral of marginal cost function from…

Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

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Q: Evaluate the integral using the appropriate substitution. You must use a substitution for this…

A: Given query is to find the integral.

Q: x = -2t 1- y = z – 8 and l2 2 - 3 Given: line lı : 4 y = 2 + 2t % = 6 + 2t 2. Find the equation of a…

A:

Q: 4 Which formula would be used to calculate the trapezoid approximation of L dx using five…

A: We have to use trapezoidal rule. Option B is correct.

Q: 2. The integral S,n(4 - y²)?dy represents the volume of a solid. Sketch the region, rectangular…

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Q: Sólvé thé équátión ón the interval U30<2T. 0<2x. 4 sin 0 + 5 = 7

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Q: Find the linearization L(x,y) of the function f(x,y) = e 4x cos (7y) at the points (0,0) and 0,- ...…

A: To find the linearization Lx, y of the function fx, y=e4x cos7y at the the points0, 0 and 0, π2.

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: x° 16x6 -24x3 +9 dx

A:

Q: 3 10х° -34х + 4 2x-4

A: We have to find the long  division

Q: Find the Taylor polynomial of order 3 generated by f at a.   ​f(x)=x2​, a=9

A: Use derivative and taylor polynomial got finding the unknown

Q: Find the derivative. Write the final answer without negative or fractional exponents. a. f(x)=…

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Q: Calculus What is the inverse of f(x)= x^3 +x -4

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Q: Find the arc length of the curve on the given interval. (Round your answer to three decimal places.)…

A: Arc length of the parametric curve :                 L = ∫αβ dxdt2+dydt2 dt.

Q: 3e" da V4-e2a

A: We have to find out the integral

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

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Q: Solve the differential equation dy + y = 4xy³, y(0) = dx %3D 1.

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Q: f(x) = S, 0 1+x2

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

A:

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

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Q: C Fnd the firet order parho derivohve of 4.5 f(x,y,2): W y-16y²23+ 43x hCs, t) =° t*In ts) + 9. 1. =…

A: Given