There is a line through the origin that divides the region bounded by the parabola y = 4x – the x-axis into two regions with equal area. What is the slope of that line? 5x? and -

Q: Consider the following planes. 3x + 4y – z - 56 x - 8y + 2z = 0 (a) Find the angle between the two…

A: Find the angle between the two planes..

Q: The value of the integral I = is required in the development of the normal probability density…

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Q: Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed…

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Q: Find the Laplace transform of: f (t) = v1+ sin t + (7t)14 + t² sin 2t

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Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8…

A: The expression for the arc length of the curve is: L=∫x1x21+dydx2dx   Given; y=8x23x1=1 & x2=8

Q: We know that y dy? arctan (e*+1) so whats the value for dx 1 a) e2a+2 +1 1 Ob) els+1)* +1 Need This…

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: Find the curvature and the radius of curvature at the point t = 0. %3D x = e' cos(t), y = e' sin(t),…

A: r(t)=et cos(t) i+et sin(t) j+7et kr'(t)=[etcost-etsin(t)] i          +[etsint+etcos(t)] j +7et k…

Q: 2 Find the Inverse Laplace transform f(t) if given the Laplace Transform function 1 F(s) = using…

A: Use partial fraction

Q: Use the arc length formula to find the length of the curve  y = 3x − 5,   −2 ≤ x ≤ 3.  Check your…

A: Given : y=3x-5 ,   -2≤x≤3   To Find : Arc length

Q: 1. Find the equation of the tangent line to the curve x = e', y = et at t = 1.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Assume the cubic function f(z) = ar+ b +cz+d, %3D has a relative maximum value of 3 at z =-2 and a…

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Q: Indicate whether the following statement is true or false. P(x) Let P (x) and Q (x) be polynomials…

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Q: The current population of a small town is 2376 people. It is believed that town's population is…

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Q: 1. F'(x) = 2x ; F(1) = 2 2. F'(x) = 4x +1; F(2) = 6 3. F'(x) = 3x² + 2 ; F(-3) = -32 4. F'(x) = 4x³…

A: Apply integration both side with respect to x

Q: 10 (5, 10 -x, x>5 x55 Use geometry to evaluate f(x) dx for f(x) = O 12.5 O 25 37.5 Cannot be found

A: Given that fx=5,x≤510−x,x>5 To evaluate ∫010fxdx

Q: Find the inverse of the function. f(x) = 9-2x^3 f^-1(x) =

A: THIS QUESTION CAN BE SOLVED USING THE CONCEPT OF INVERSE OF FUNCTION.

Q: The shaded region between the graphs of 2x2 + 20 and y = 3x – 15 is displayed - - below in orange.…

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Q: Using the method of cylindrical shells, set up but do not evaluate an integral for the volume of the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: z = 16 - x2 - y2 10 -8 1768 46 8

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Q: Use Green Theorem to Evaluate y x'dx – x²dy where C is left half of x² + y? = 25

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Q: Find the arc length of the parametric curve. 8 cos(t), y = 8 sin(t), z = 6t; 0<t<T x = L =

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Q: Use finite approximation to estimate the area unde the graph of y = 5x² and above the graph of f(x)…

A: As per guidelines, I can answer maximum three subparts if a question. Since you have asked fot…

Q: ne area Of Lhe region

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: Find the solution of the following BVP given that y(0)=2 and y(1)=0. d’y_12dy. dx +36y = 0 dx

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Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

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Q: lim x-00 1 with a a real constant different from 0, consider the Consider the limit following…

A: We have to find out the correct answer

Q: For what vaules of x in the interval [0,2π) does the fraph of g(x)= (√3)x+2sinx+7 have a horizontal…

A: For horizontal tangent,first derivative must be zero

Q: Find the equation of the line parallel to: a. 13x + 9y + 180 = 0 b. 2х-7у-35%3D 0 x+ 10y-11 0…

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Q: Use the arc length formula to find the length of the curve y = 3x – 5, -2sxs 3. Check your answer by…

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Q: Find the linear approximation at x = 0 to each of f(x) = (x + 1)², g(x) =1+ sin(2x) and h(x) = e2*.…

A: To find the linear approximation at x=0 to the given functions using the formula:…

Q: 3x 4x e, y = e", and Sketch the region enclosed by y = x = 1. Find the area of the region.

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Q: Find T(t) and N(t) at the given point. r(t) = 3 cos(t)i + 3 sin(t)j + tk; t= 2

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Q: Indicate whether the following statement is true or false. The function f (x) = |x| is continuous at…

A: Solve the following

Q: S 4x53x dx 3.)

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Q: Evaluate the triple integral. zy sin(yz) dV , where G is the rectangular box defined by the…

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Q: Let y = (2x + 2 sin(x))“. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

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Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: To find maxima/minima of the function: f(x,y)=x2+2y2-3xy with constraint g(x,y)=x+y-24=0

Q: x* – 1 f. lim x-1 x In x sin 3x g. lim x-0

A: (f). Given: limx→1xx-1xlnx   As we know that; The Chain rule: fgx'=f'gx·g'x

Q: Use the Fundamental Theorem of Calculus to find the "area under the curve" of f(x) = 4x + 7 between…

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Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly…

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Q: How can we write out the summation of this notation

A: Topic:- simplification

Q: Use a double integral to find the volume under the plane  z=32x+yz=32x+y and over the rectangle…

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Q: pproximate using differentation:  e0.99 Please show step by step solution.

A: This question can be solved using the concept of approximation using derivatives.

Q: 3 The series E converges if n=2 (n+ 1)P (n – 1)ª (a) p+q1 (c) p+q=1 (a) p+q=2 (e) -1<p+q<1

A: Solve the following

Q: The volume of a torus (doughnut or bagel) with an inner radius of a and an outer radius of b is V -…

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Q: Find the area of the shaded region. r = Vcos 20 r = 14 cos 0 NOTE: Enter the exact answer. A =

A: Area of shaded region .

Q: - x)dx 1 X 2 х +x+1

A: