Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). v = (0, 12) a =

Q: Applications of Integral calculus 3. The following curves bounds a certain area: y = 4x – x2

A: Area bounded by a curve y=f(x) on [a,b] is given by, A= ∫abydx

Q: 4 is a geometric series or not. If so, determine if the series Determine if (-3)" n=1 converges or…

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Q: A) Write the DE that describes the model and solve it. B) Determine the time needed for the number…

A: Follow the procedure given below.

Q: Integrate the ff.

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Q: Suppose that the bacteria in a colony grow unchecked according to the Law of Exponential Change. The…

A: Given:    Since we have given that Number of bacteria initially = 1   It triples in number every 30…

Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1)

A: To find the gradient of the function at the given point.

Q: (k) (In n)n n> 2.

A: k. 1ln nn ,  n≥2let, un=1ln nnun=1ln nn12=1ln nn2by cauchy roots testlimn→∞  un1n=limn→∞  1ln…

Q: Let a = ci + jand b = 2i + 10j. Find c so that a and b are orthogona C = i

A: Given: a=ci+j b=2i+10j.

Q: A body moves along a horizontal line in accordance to s t + 9t2 + 24t. Find the total distance…

A: Given query is to find the distance traveled by the body

Q: S 4x* sin2x dx A (2xª + 6x² + 3) cos 2x + (4x³ + 6x) sin 2x + C C (2xª – 6x² • 3) cos 2x + (4x³ –…

A: Integrating by parts : ∫u.v dx =u∫v dx -∫dudx∫v dxdx dxndx=nxn-1 ∫cos(ax)dx =1asin(ax)+C ∫sin(ax)dx…

Q: Determine if the following statement is true or false. The lines L1 and L2 are skew. L:x = 10 + 3t,…

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Q: indefinite integrals: Show complete and detailed solutions. Express your answers in simplest form…

A: Product Rule of integration : ∫u.v dx =u.∫vdx -∫dudx∫v dxdx ∫yn dy =yn+1n+1+C ∫cosu du =sin(u) +C

Q: The rate of change dP of the number of wolves on an island is modeled by the following differential…

A: Let's find.

Q: Find the directional derivative of f(x, y, z) : 4y at P(3,1, –2) x + z in the direction from P to…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of  PQ.…

A: Given problem:- Find the directional derivative of the function at P in the direction of PQ. f(x, y)…

Q: Find the solution set of the inequality 5x2 – 2x + 12 < 6x² – 3x – 18. - Select one: а. [—5, 6] b.…

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Q: In the cost function below, C(x) is the cost of producing x items. Find the average cost per item…

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Q: Q3. Evaluate the integrals below. For each integral, first calculate the related indefinite inte-…

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Q: x³3-* dx -x³3-*In (3) + 3x² 3¬× ln²(3) – 6x 3¬×ln³ (3) + 6 3¬× In*(3) + C A B -x³3¯* ln(3) + 3x² 3¯*…

A: Let's find.

Q: Find the area of the triangle with vertices P(1, 5, –6), Q(0,0,0) and R(3,5, 1). NOTE: Enter the…

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Q: In Circle H, Segment RA is a diameter Theorem 100: Inscribed Quadrilateral Theorem Quadrilateral…

A: To prove Theorem 110:  If two chords are equidistant from the center of the circle,  then the two…

Q: Find the constant a such that the function is continuous on the entire real line. x 2 1 f(x) = x-4,…

A: Find your answer below

Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

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Q: 1 cos(sec-x) dx 2/V3 xVx²-1

A: Let's find.

Q: Recall from calculus, if a function is differentiable at a point c, then it is continuous at c, but…

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Q: Which of the functions I-III meet each of the following descriptions? There may be more than one…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 10. * S sin(In x)dx 1 C x sin(Inx) – cos(Inx) + C 2. x sin(Inx) – cos(lnx) + C 1 x sin(lnx) +…

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Q: SOLVE the following DIFFERENTIAL EQUATIONS using appropriate method. 1. (3x'+ 2y)dx + 2xydy=0

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: ²+6x +8 a. f(x) : x + 2

A: I am attaching image so that you understand each and every step.

Q: Determine whether the following functions are continuouuus or not. Are not, classify them as…

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Q: SEATWORK Solve two problems; one problem from #1 and one problem from #2. Submit clear and upright…

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Q: Determine whether each improper integral below converges or diverges. dx 3. S. x* + 2x – 3

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Q: 2 +y? +? inge muitipilers to find the maximum and minimum values of f(x, y) = 2x + y – 2z subject to…

A: We are using Lagrange multipliers method

Q: Please answer each question with solution.

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Q: 1. Let Ā = (-1,2, 3) and B = (4,–3, 1). Find the following. c. [2Ã] – |3Ē| d. [2Ã + B|B a. JĀĪĒ –…

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Q: |(x + 1)°sinx dx -(x + 1)³ cos x + 3 (x + 1)² sin x – 6 (x + 1)cosx – 6 sinx + C (x + 1)³ cos x – 3…

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: R Examine the discontinuity for each of the following functions. If the discontinuity it removable,…

A: The objective of the question is examined the continuity and removal discontinuous.

Q: The series > cos" (2) is divergent. n=1 This statement is true by the test for divergence. This…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 4, 3) (b)…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Find your answer below

Q: definite integrals: Show complete and detailed solutions. Express your answers in simplest form…

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Q: 1+ 4" 1+ 3" n=1

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Q: Eliminate the parameter on t to write the parametric function as a Cartesian equation in y = form.…

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Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: Please see the answer below.

Q: Evaluate the integral of· if it has an upper limit of 1 and a lower limit of 0. (x+1)®

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Q: 2x+5 (d)Using the method of Partial fractions find f dx x2-8x+7

A: Let's find.

Q: Suppose that it is given to you that f′(x)=(x+5)(10−x)(15−x) 1.The first inflection point (from…

A: Given that,     f'(x)=x+510-x15-x

Q: アrova solution to if ulx,t)= (sin (x- 6 )-Sin (x+6)) tion equa %3D

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Q: y = Vx +1(3– x)* (x- 3)(5x + 1) 2/x +1 b Find the x-coordinates of all points on the graph of y…

A: To find the derivative of given function.