Find the coordinates of the point (x,y) on the curve y=2x+1 that is closest to the point (6,3) .{ Hint: find the minimum of the square of the distance) . use a derivative test to verify that your answer is optima

Q: Consider the function f(x) = 2sin(x2) on the interval 0 ≤ x ≤ 3. (a) Find the exact value in the…

A: Given f(x)=2sinx2    0≤x≤3

Q: The volume (V) of wood in a tree varies jointly as the height (h) and the square of the girth (g).…

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Q: Use spherical coordinates. Evaluate JJJ √x² + y² + z² dV, where E lies above the cone z = x2 + y2…

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Q: Consider the following. f(x, y, z)=√x² + y² + to + y² + ₂2 E (a) Express the triple integral x² + y²…

A: Using spherical coordinates, x=ρsin(φ)cos(θ)y=ρsin(φ)sin(θ)z=ρcos(φ)x2+y2+z2=ρ2,dV=ρ2sin(φ)dρdφdθ…

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A: Given

Q: 21. y = cos²x³

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Q: A shop is open 9 AM - 7 PM. The function r(t), graphed above, gives the rate at which customers…

A: SOLUTION:-   Given, a shop is open 9 AM - 7 PM.  The function r(t) gives the rate at which customers…

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Q: Use the factorization A = PDP to compute A, where k represents an arbitrary positive integer. -5 24…

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Q: 2. the line x = 3. Non-Calculator: Let R be the region in the first quadrant bounded by the graph of…

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Q: Evaluate the indefinite integral below. 7 [m²+1 dm

A: Given;

Q: The vertices of a triangle have coordinates (6,8), (-9,14), determine if the triangle is a right…

A: The vertices of a triangle have coordinates (6,8), (-9,14)

Q: I need to apply the divergence test to the series. However, I am stuck, how do you take the…

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Q: 7 = (–9,6, –1) ≤ R³

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Q: The MacLaurin Series for tanx is tan x = x + 3 + 2 15 tô + 17 315 x +. and it has a Radius of…

A: MacLaurin Series for tanx is given as , tanx=x+13x3+215x5+17315x7+····· and Radius of convergence of…

Q: Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values…

A: Given sin(x)=x-x36

Q: Solve log_(4)x+log_(4)(x-1)=2. Round to the nearest thousandth.

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Q: Find the equation of the line tangent to the parametric curve c(t) = (ln t, t² + t) at the point t =…

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Q: Estimate ³√26 by using a linear approximation x=27 of f(x)=³√x about the value

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Q: Determine if y = ²x − x + 1 is a solution to y' - 2x = −3+ 2y. - Select the correct answer below: O…

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Q: 1. Lim 2 x+3x+1 7x²-2x+4

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Q: If you make $43,700 and get $2300 raises each year, in how many years will your salary double?…

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Q: Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or…

A: The solution is shown in step-2

Q: f(x, y): = x³+y³9x² 27y + 5 and classify each as a local maximum, local minimum, saddle point, or…

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Q: Let a„(x) = (n + 1)²™”, and define f(x) = an(x). n=0 a) Evaluate the following quantities: lim h(x)…

A: We have;

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm²/min, find the rate (in…

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Q: TC 0 럭 In x X dxdy

A: ∫0π∫0ylnxxdxdy

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 9…

A: The given double integral is  ∫09∫081-y2(x2+y2)dxdy We have to change the Cartesian integral into an…

Q: If two resistors with resistances R₁ and R₂ are connected in parallel, as shown in the figure, then…

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Q: 8- Evaluate S² -2-y Jy x+y dxdy

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Q: Find or evaluate the integral. /sec² sec² (4x) dx

A: let V=∫sec2(4x)dxwe know  (i) sin2x+cos2x=1(ii) tanx=sinxcosx(iii)  d dx(ab)=b×d dx(a)-a×d dx(b)b2

Q: Evaluate the indefinite integral below. Hint: Use algebra properties to simplify the function first.…

A: Evaluate the indefinite integral below. Hint: Use algebra properties to simplify the function…

Q: 1 as Compute the first four partial sums S₁, ..., S4 for the series having n th term an starting…

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Q: A particle moves along the curve below. y=√1+x³ As it reaches the point (2, 3), the y-coordinate is…

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Q: 5. Evaluate the triple integral fff 6xy dV, where E lies under the plane z = 1+x+y and above E the…

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Q: Write the given system as a matrix equation and solve by using the inverse coefficient matrix. Use a…

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Q: Please help me find cosh(2) and cosh(0)

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Q: 13) Suppose we know that F'(x) = x cot (x). Simplify [25 by expressing this integral in terms of the…

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Q: Minimizing Construction Costs The management of the UNICO department store has decided to enclose a…

A: let  x= length of steel fence        y= length of one side of pine boards   given:  xy=933 y=933x…

Q: 2. Let f(x) = x50 ³x¹ sin(x³). Calculate f(137) (0). You may leave your answer indicated in terms of…

A: Here we find f137(0) = ?

Q: 2. (a) Find the horizontal and vertical asymptotes of the graph of the function f(x) = 5x+7 2x-3 (b)…

A: Part a Given f(x)=5x2+72x-3 We are required to find: The horizontal and vertical asymptotes of the…

Q: Find the directional derivatives of the following functions at the specified point for the specified…

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: III. Find the values of the constants a and b that make the function f continuous on (-∞, +∞ ). [3x…

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Q: Consider the following. y 16₁ x ² ² + · dA, D = {(x, y) 10 ≤ x ≤ 7,0 ≤ y ≤ √x + 1 Rewrite the above…

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Q: K Pertorm the indicated operations. Leav (7-(x+1)/(x))/(9+(x-1)/(x+1))

A: To perform the indicated operations, we need to simplify the given expression. First, let's simplify…

Q: a) What is the z-component of a vector parallel to the xy-plane? Explain. b) Find all unit vectors…

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Q: Use cylindrical coordinates. Evaluate JJJ (x - y) dv, where E is the solid that lies between the…

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Q: Part 1: Partial Fractions Use the partial fractions method to express the function as a power series…

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Q: Draw the spin field F = and vertical components at a representative assortment of points on the…

A: We need to find components.

Q: Find the difference between the upper and lower estimates of the distance traveled at velocity f(t)…

A: velocity ft=30-t2interval 1≤t≤4subdivision =n=500