Find the exact absolute maximum and absolute minimum of h(t) = cos(2t) + √3 sin(2t) on [0,1]. Show all your work.

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Q: 1. Let v (4, -2,-4) be a vector in R³. (a) Find a unit vector in the direction of v. (b) Find a…

A: Given vector v→ = 4i -2j -4k

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Q: Given f(x) = ln(3x2 + 8x + 2), find the equation of the line tangent to the graph of f at x = 0.

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Q: •Evaluate the ff. dx 3x²+12x+15 T.

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Q: Find the distance between the skew lines: x = 5+7t, y=3+7t, 2=8-9t x = 1-t, y = 6, z = 5+8t NOTE:…

A: The given skew lines: L1:  x=5+7t,  y=3+7t,  z=8-9tL2:  x=1-t,  y=6,  z=5+8t

Q: Was this answered?

A: Given:- At=2.3sinπ6t+9.25 ⇒At=The average monthly rainfall in centimeters

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Q: Two vertical poles of heights 60 ft and 80 ft stand on level ground, with their bases 100 ft apart.…

A: Given : their bases 100 ft apart BD = 100 ft let BC = x  CD = 100 - x

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Q: a) Find all of the critical points of x2 - x - 1 b) Find all of the critical points of x3 - 3x - 2

A: We have to find the critical points.

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A: Answer: The solution is given below:

Q: 4. Differentiate = ex) in (ex + xe (b) find dy by implicit differentiation 2 ху √x² + y²

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Q: Consider the functions graphed below. C (0,b) (1,1) (a) Find the slope of the line. slope = Answer…

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, -6) +…

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Q: This problem illustrates the Second Derivative Test. Let f(x) = - arctan(x²) + 3 . (a) Find f'(x) =…

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Q: Assume that it costs a company approximately C(x) = 800,000 + 360x + 0.0005x2 dollars to manufacture…

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Q: Q3 Find the exact limit. lim x48 sinh(22) ex

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Q: Find the slope-intercept form of the equation of the line tangent to the graph of fx=3*сos лx at the…

A: To find the slope-intercept form of the equation of the line tangent to the  graph of fx=3-x cosπx…

Q: 1. Find the Cartesian coordinates a. 1 2 I b. -√2₁. 2 3 π

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Q: Find the intervals on which the function is increasing or decreasing. (X) =283 - 6x2-48×+ 12 List…

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A: The given data is: C=5aq+3bq

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A: We need to approximate the area under f(x)=e-x2 from x=5 to x=22. So, here, a=5 and b=22.

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A: Given equation:- x2+y3-3xy2=-1

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A: Given Profit function:- Px=30x-0.3x2-250

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A: Since the student has posted multiple questions and does not mention any specific question, so we…

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Q: Differentiate the function. f(x) = x²(x + 8) f'(x) =

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Q: K Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation…

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Q: Differentiate the function. g(t) = 4t-1/8 g'(t) =

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Q: Let R be the region in the first quadrant bounded by the graph of y = e, the z-axis, the y-axis, and…

A: Given :- Region R in the first quardrant bounded by the graph y=e-x,the x axis , the line x=b

Q: X -4 -2 0 2 4 36 6 10 0 -10 -6 ind h(f(g(0))) X ind k(3) if k(x) = . -3 -1 0 1 3 x²g(x). g(x) -7 -5…

A: f(-4)=6 f(-(-4))=f(4)=-6=-f(-4) same for other values of f(x) hence f(x) is odd function    g(x) is…

Q: 3√/t-1 S (³√t=¹) dt = 3 − 2t + c - C

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Q: Find the distance x = 2 + 6t, y x = 9-t, NOTE: Enter the exact answer. D = [ between the skew lines:…

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Q: e + Ax = A= + cx Solve for y:

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Q: The region bounded by y = x and y = x² is rotated about the line x = 2. Which of the following would…

A: To find the volume of the solid obtained by rotating the region bounded by y=x and y=x^2 about the…

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Q: A function fis given, and the indicated transformations are applied to its graph (in the given…

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Q: 5. Find the points on the graph of f(x) = x³ - 3x where the tangent line has slope 0.

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Q: Find the derivate of this function]: a) f(x)= 9x²³+24x² - T F'(x) = b) f(x) = 4x³ + 9x²-9. F'(x) =…

A: (a)  f(x)=9x3+24x2-πd dx(xn)=nxn-1d dx(constant)=0

Q: Solve the following differential equation by finding h and k so that the substitutions x=u+h, y=v+ k…

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Q: LATIHAN 1 1. Obtain the cartesian equation of the curve by eliminating the parameter a. x = 3t ; y =…

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Q: 4. Find the exact and the approximate value of x: 2* = 5*-1. Round answer to three decimal places. N

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Q: Find the following limit. lim V

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Q: Write the parametric equations for the tangent line to the curve of intersection of surfaces…

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Q: Consider f(x) = x²(7 - x)5. (a) Find f'(x) and factor your answer completely. f'(x) = 67228x³ -…

A: To find the critical points of f(x), we need to find where f'(x) = 0 or where f'(x) is undefined. To…

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Q: (d) 4x²y" + y = 0, (e) y" + 16y = 0, Y₁ = √√x ln x Yı Y₁ = cos(4x)

A: see below the answer and calculation