Find the shortest distance, d, from the point (4, 0, -4) to the plane x + y + z = 4. d =

Q: Evaluate /| F - d5 , where F = and S is the helicoid with vector equation r(u, v) 0 < u < 4, 0 < v...

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Q: 49-60. Evaluate each limit. cos x - 1 57. lim 0 sin? x

A: The given limit,     limx→0cos x-1sin2x

Q: Find the area of the shaded region in the given graph.

A: This question can be solved using the concept of area under curve using definite integral.

Q: a. Find the equation of the line tangent to the following curve at the given value of x. b. Use a gr...

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Q: S10ze +ldr= Select one: O z'e* +l + c O 5e²+1 + c O 4re+1+ c O 6e +1 + c O None of the other choices...

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Q: Find  f '(x). f(x) = (x2 + 4x)(x + 3)

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. Зп ...

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Q: A 12-lb weight stretches a spring 2 ft. The weight is released from a point that is 1 ft below the e...

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Q: For the cost function, find the marginal cost at the given production level x. State the units of me...

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Q: Estimate the area under the graph 1 of f(x) = from a = 5 to x2 +1 b = 13 by using n = 4 rectangles o...

A: The given function,   f(x)=11+x2 from a=5 to b=13 by using n=4 rectangles

Q: The weak Axiom of Revealed Preference is satisfied by the choices of demand bundles xD(p) at any com...

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Q: Evaluate the following improper integral. Give an exact answer. (Remember, the natural exponential f...

A: Topic:- definite integration  

Q: || x? zdS, where S is the part of the plane z = 1 + 4x + 3y above the S. Evaluate rectangle [0, 3] x...

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Q: Determine the value of x of: (x² – 1 x < 1 f(x) = { x – 1 .2 x21

A: Given query is to find the the value of x.

Q: Find the directional derivative OF the Function in the divection U = Cos e it Sin e i OF the unit ve...

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Q: Given: x2 dx Find: Formula o fa"du q"du o fe"du "du

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Q: Assume that sin(z) equals its Maclaurin series for all x. Use the Maclaurin series for sin(72) to ev...

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Q: 2x хе 2x +c Select one: O True O False

A: We will integrate the function and will evaluate left hand side as:-

Q: The graph of a rational function f is shown below. 10 4- 2 -6 -4 4 6. -2 a. What is the horizontal a...

A: The graph of the function y = f(x) is given as

Q: What is the reversed order of integration of dydx ?

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Q: 3 x lies in the third quadrant, find the values of other five If cos x = - 5' trigonometric function...

A: In third quadrant tangent and cotangent are positive.

Q: Consider the following image. 10 -10 -5 10

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Q: Find all complex solutions (real and non-real). (Enter your answers as a comma-separated list.) x^3...

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Q: Let f(x) = 4e"+2 + e-3. | f'(0)

A: Question is solved.

Q: Find the derivative of the function.   g(x) = 9 3   x + 8

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Q: Given f(x) = x- 1 and g(x) = x2- 1 Find and simplify the following 1. g {f (x)} 2. g-1(x)

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Q: Determine the value of x of the discontinuous function: х — 1 f (x) 3D {3х — 3 (-4x + 3 x 3 -

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Q: emaiminy Tme. Unin Determine a formula for the general term an of the sequence {an} = { 3 12 27 48 7...

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Q: dx Evaluate 6e* cos (3e *) O 2 [In |sec(3e-x) + tan(3e-|] + C In |sec(3e-M) - tan(3e-|] + C O -18 [I...

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Q: Consider the following. br (a) Set up an integral for the volume a solid torus (the donut-shaped sol...

A: We have to set up an integral for the volume of solid integral.

Q: At which point(s) is the function shown discontinuous? Select all that applies. O-1 O1 02 04

A: The graph of a discontinuous function cannot be made with a single stroke of the pen, i.e., once we ...

Q: Question 1 Find the derivative and simplify y cotVt-1 Oy-- Oy= - 2tt-1 1 2t/t-1

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Q: Calculate the area of the figure given by the law of the mean of two bases 15 :8 13 10 11 8. 8 8. 8.

A: Area of trapezium =12(sum of two parallel sides)×heightArea of triangle=12×base×heightArea of figure...

Q: complementry function for this DE  12.7y" + 68.58y' + 153y = 0.289(y+1)

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Q: Find the exact value of the slope of the tangent line to the graph of 2 – x? – a² + 3xy – 3y = 1 at ...

A: Slope of the tangent line , m=dydx du.vdx = u.dvdx +dudx.v dxndx=n.xn-1

Q: csc S- |cot2즐x)-4cot(를x) +4 Given: Find: u cot -2 O ca) cot 4cot x+4 cot +4

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Q: f(x) = x2 + 7x +  5 x f '(x) =

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

Q: lim +2-3t メー→3 十-3

A: Topic:- limits

Q: secx 7. When does the graph of the function f(x) have a horizontal tangent? 1+ tanx

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Q: If $20,000 is invested in a savings account offering 3.5% per year, compounded continuously, how fas...

A: We have to find how fast balance will grow per year after 4 year

Q: List the first five terms of the sequence a, = 3, a, = 1, an+1= 5an – 2an1 a1= Number a2 = Number az...

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Q: Graph the function, not by plotting points, but by starting from the graph of y = ex in the figure b...

A: Question : Graph the function, not by plotting points, but by starting from the graph of y = ex in t...

Q: Write an equation of the tangent line to the graph of f(x) 3x at x = +1. %3D 1+2x2 For what value(s)...

A: Given that fx=3x21+2x2 Solution :fx=3x21+2x2f'x=6x1+2x2-4x3x21+2x22if f'x=06x1+2x2-4x3x21+2x22=06x1+...

Q: dx Evaluate 6e* cos (3e *) -In |sec(3e ) – tan(3e |] + C O 2 [In |sec(3e-x) + tan(3e-)|] + C -18 [In...

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Q: Find the derivative of the given. f(x)= cos x cot x let g= cos x and h= cot x. Then, g'= -sin x an...

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Q: Calculate the iterated integral. 36(u – v)³ du dv

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Q: Determine the value of x of: * (x² – 1 f(x) = { x – 1 x < 1 .2 x 2 1

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Q: List the first five terms of the sequence : (-1)"n an = n! +2 a1 =Number a2 =Number a3 = Number a4 =...

A: Given:            an = (-1)nnn!+2⊙Then, for a1  put n=1 in an:           a1 = (-1)1(1)1!+2Hence,    ...

Q: Find the equation of the tangent line to the curve (a lemniscate) 2 2(a? + y?) = 25(æ² – y²) at the ...

A: Topic:- application of derivatives

Q: Evaluate the integral. tan(10 x) sec*(10 x) dx +C

A: