Determine two positive values such that the sum of the two numbers is 105 and the product of the first number and the square of the second number is a maximum. Enter the solutions using a comma-separated list. Determine the maximum value. Question Help: Message instructor Submit All Parts

Q: ciderivative of F(X, for x = 0.784 and y = 0.7. Note: Use

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Q: Suppose that f(2) = -5, g(2) = 3, f '(2) = -2, and g'(2) = 4. Find h'(2). (a) h(x) = 4f(x) – 3g(x)…

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Q: Find an equation of y =

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Q: 7.) Without using decimals, common denominators, or cross multiplication, be convincing of which…

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Q: 10x Find a power series for f(x) = |x| an. (x² + 1)² n=1 Hint: First, find the power series for…

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Q: Question 3 <0 <t Given Cos(0): 5 and 2 ,what is the value of cos(20)? -21 A 5 B 7 25 16 D 25

A: This question is based on Trigonometric equation.

Q: Find dy/dx by implicit differentiation. tan(x – y) 7 + x2 y' =

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Q: 4. Use §4.4 guideline to sketch the curve: y = x- 4x/3. A). Domain, Symmetry, Asymptotes,…

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Q: Given the following vectors a =(-1,-2),5 =(-3,-4),c = 2,-1), d = (-4,3) Use the dot product and…

A: We have to use dot product and scalar multiplication to find the relation between vector b and d.

Q: Question The base of a triangle is shrinking at a rate of I1 cm/s and the height of the triangle is…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Find the supply equation using the given information. (Let x be the number of items.) At a price of…

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Q: Find the interval of convergence of n 2(-1)". 64" n=0 (Give your answer as an interval in the form…

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Q: Use the equation x" for |x| < 1 to expand the function 6. in a power series with center c = 0. 1-x…

A: To determine the interval of convergence.

Q: Identify the form of the partial fraction decomposition of the rational function -3x2+10 x²(x+-25)…

A: Given that-3x2+10x2 x4-25Solution:if cxx2-a2…

Q: Find the interval of convergence of 5 (x - 9)" In (5n) n=2

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Q: 2+w4 dw w3+9w

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A: Here, the equation of the given plane is: -x+5y+z=6 Therefore, the normal of plane is (-1,5,1). Now,…

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Q: x-4 17. f(x)%D at x 1 x-2

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Q: x'+3x +3x+1 (3) (i) Find lim x+1 2x +3x –1

A: In given function on putting x = -1 it gives ( 0/0) indeterminate form .  Hence first we factorize…

Q: Consider the following. u = -6i – 2j – 4k, v = 2j + 2k %3D (a) Find the projection of u onto v. (b)…

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Q: 1.e -9- -2 4,0 2

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Q: Estimate the slope of the tangent line at the point t = -6, for f(t) = 4t – 2. (Give your answer as…

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Q: Astivity 3 tind the dertve of 2メー3 う×ース enuing the definitiom -

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Q: Find the volume of the solid of revolution formed when the area of the region bounded by y3Dx2,…

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Q: 1+cos5x 4. Evaluate y'for y = and simplify the answer sin5x

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: dy Use implicit differentiation to find da y? + 8z = 3y – 5a? dy dx

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Q: Evaluate the triple integral. 3xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: To apply this test we must first find Y'(N). Doing so gives the following result. kN Y(N) 16 + N2…

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Q: Use a graphing utility to graph the function on the closed interval [a, b]. x) - Ixl - 3, (-7, 71 -2…

A: topic - Rolle's theorem

Q: -4 -2

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Q: 3. Find the interval fconvergence of the Sevies : 1-3(x-4) + 9 x-4)-..

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Q: Use the method of Lagrange multipliers to find the largest volume of a box with no top subject to…

A: To find the largest volume using the lagrange multiplier .

Q: Use the definition of a normal subroup to prove Proposition 2.3.7: IfGis an Abelian group, then…

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Q: Find lim,0 f (x)

A: The objective is to find the limit at 0.

Q: 12 22, 23 , 2* 5*6*7 *8 * 3. Test the series

A: D' Alembert Ratio Test: Let ∑n=0∞un be a series of positive real numbers such that limn→∞un+1un=L…