Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 17 + 4x - x², [0, 5] absolute minimum value

Q: Find the derivatives of the following: 1.) x* + 2y = 6x 2.) f(x) = (tan 5x) (x + 2)²

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Q: Find for the given function. dz? w= 10z2 ez dz 2)

A: Use dervative rule

Q: Find polar coordinates (r, 0) of the point (1, -V3), where r <0 and 0 s0 < 2m

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Q: sin³xdx ? 1- cosx Which Jof the following is one of the correct steps to evaluate A) None B sinydy +...

A: Just I have simplified the given integrand function and find that option (B) is correct.

Q: ,In sec²(sin2y)dy can be evaluated by writing it as sec2y ! / sec²( sin2y) - 2 cos2ydy S. | sec2( si...

A: To simplify the given integral.

Q: A rock is thrown into a still pond. The circular ripples move outward from the point of impact of th...

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Q: Find the critical points of f(x) = x³ – 21x² + 72x and use the Second Derivative Test (if possible) ...

A: f(x)=x3-21x2+72xFor critical pointDifferentiate the function f'(x)=3x2-(21×2x)+72f'(x)=3x2-42x+72Tak...

Q: У7" — 1)" (10.х n=0

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Q: Find the vector component of v = 2i – j+ 3k along b = 4i + 4j + 7k and the vector component of v ort...

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Q: urrent An oil slick on a lake is surrounded by a floating circular containment boom. As the boom is ...

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Q: 1. y (x3 +3)5

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Q: If f'(x) = 12r + 3z² and f(1) = 7, find f(x) . f(x) =

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Q: 3. S cot° (3æ) csc* (3x)dx CSC

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Q: Evaluate the following: 1. S sin³ 4xcos³4xdx

A: 1.Solution : ∫sin34xcos34xdx123∫23sin34xcos34xdx123∫sin38xdx    2sinxcosx=sin2x123∫3sin8x-sin24x4dx ...

Q: dr Let A be the area of a circle with radius r. If dt dA 5, find when 7 3. dt

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Q: Find the length of the curve defined by æ? = 2y³ from x = 0 to x = 4:|| %3D

A: We need to find length of curve.

Q: Let R be the region in the first quadrant bounded on the right by the graph of y = x – 3, above by t...

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. ...

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Q: 3. If f(x) = cos(x), determine f(125) (-T). V2 (B) 2 (A) 0 (С) 1 (D) –1 1 (E)

A: we will use nth derivative formula of cosx .

Q: 1 1 3. lim ed - 1

A: Given query is to find the limit of the expression.

Q: nd an equation of the plane that passes through the given point and is perpendicular to the given ve...

A: Given point P(2,6,-9) i.e. x1=2, y1=6 and z1=-9Given vector is n=j i.e. c=1We know that equation of ...

Q: The movement of a particle follows g(u), where g(u) h(u) and h(u) = u? + 8u + 15 and y(u) = u² + 2u ...

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Q: (D³ – Dª + 4D³ – 4D²) y = 32 cos (2æ) – 20e-

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Q: An element loses 31% of its mass every year. Find the half-life in this situation. The half-life is ...

A: We will find the half life of the element. 

Q: 3. 2- 1- ol 1 4 Let R be the region bounded by the graph of y = Va – 1, the horizontal line y = 2, a...

A: As shown taking the horizontal stripe x changes from 1 to y2+1 because  y=x-1⇒y2=x-1⇒x=y2+1

Q: Find the vector component of v = (4, – 1, 7) along b = (4, 4, –7) and the vector component of v orth...

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Q: x2 + 2 dx x° + x •T/2 5. 3 6. t cos (t) dt

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Q: If y = csc² x+ 2 , then ſ y dx = cot x + 2x + c True O False

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Q: 5. Suppuze that.the..are..a.regian.is 2 SinG 3T/4 rdrd@..sketch. the.vego.and. T/4 find the.al.RMa.

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Q: Find the formula for the nth term of the arithmetic sequence. a1 = 11, d =

A: Given query is to find the formula for nth term.

Q: Find the value of k, and write the equation. Estimate the population of the country in 2015. After h...

A: We will find the exponential function. 

Q: A plant encloser is in the shape of half of a cylinder. Find the surface area of plastic covering. L...

A: Surface area

Q: Consider the pair of savings plans below. Compare the balances in each plan after 13 years. Which pe...

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Q: A wooden artifact from an ancient tomb contains 60% of the carbon-14 that is present in living trees...

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Q: Evaluate the given integral by changing to polar coordinates: Sl. x²y dA, where D is the top half of...

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Q: dt Which of the following is one of the correct steps to evaluate ? 4e'+e 4dt 4e'+e- 2e"dt B В 21 4e...

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Q: 2. S sin° () dx

A: Integration

Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In( 6 x - 3 y), Po(-7, -4...

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Q: Find d'y/dx? given x= t² – 3, y = 2t – 1

A: First I have find the derivative of x and y with respect to t and then calculate the required deriva...

Q: Write a chain rule formula for the following derivative. for u = f(p, q); p = g(x, y, z), q = h(x, y...

A: Given a function u=f(p,q)

Q: View Policies Current Attempt in Progress Locate the critical points and identify which critical poi...

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Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the regi...

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Q: x sec(em) tan(enx) dx= sec x2 tan x2 dx A) True B) False

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Q: If y = csc² x +2, then ſ y dx = cot x + 2x + c %3D True O False

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Q: Find d^2y/dx^2 for y=2x^3-5/x^2

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Q: Suppose that Po is invested in a savings account in which interest is compounded continuously at 6.5...

A: The balance P (in $) grows at a rate (per year) is given by, dPdt=0.065P(t) ............. (1)

Q: Let a = ci + j and b = 3i + 4j. Findc so that the angle between a and b is . Round your answers to f...

A: We will use the formula of angle between two vectors to solve this question.

Q: Evalnate. the. followin..deuble.integrals.by.conver.king.b.. polar.Cto.r.dinates. Gp xpx Sf- Ans.: A...

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Q: Sketch the graph of the level curve corresponding to z = 6 for the following function. z = f(x, y)=9...

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Q: Let a = ci + jand b = 3i + 4j. Find c so that the angle between a and b is %3D Round your answers to...

A: Given a = ci + j and b = 3i + 4j. The angle between a and b is π6. We have to find the value of c.