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Calculus

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Q: Complete the following statement. If dy/dx is large, then smallchanges in x will result in relativel...

A: According to the question, we have to complete the statement, If dydx is large, then smallchanges in...

Q: Let f(x) = √x and g(x) =-x/2 +2 Find f(g(x)) and write its domain in interval notation. a) f(g...

A: We first find the combined function by using the given functions. f(g(x))=f-x2+2=-x2+2Answer(a): f(g...

Q: Trigonometric integrals Evaluate the following integrals. ∫cot5 3x dx

A: Evaluate: ∫cot53xdx

Q: 1 r(t) = (t sin t, (2t)³/2, t cos t), 0 < t < 2n. 3

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Q: Find the degree of the polynomial. 3x2 - 5x + 4

A: 3x2-5x+4

Q: Find the volume of the solid whose base is the region in the xy-plane that is bounded by the parabol...

A: Volume below z=f(x,y) and above region R IN x-y plane is given by: V=∫∫Rf(x,y)dA where dA is the Ar...

Q: 36 please

A: Given rt=cost i +sint j +2t k , t=π3

Q: decide if the given statement is true or false,and give a brief justiﬁcation for your answer.If true...

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Q: Compute the following double integral over the indicated rectangle.

A: Given: ∬sin2x-11+6ydAR and R=π4,π2×0,1 To find: The value of integral.

Q: Use a table of values to estimate the value of the limit. V x + 25 5 lim

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Q: Find an equation of the tangent plane to the given surface at the specified point. z= 2(x = 1)² + 6(...

A: Given: The equation of surface is z=2(x-1)2+6y+32+1, and the given point is 3,-2,15 To find: The equ...

Q: Tangent planes Find an equation of the plane tangent to the following surfaces at the given points (...

A: Find an equation of the plane tangent to the following surfaces at the given points (two planes and ...

Q: Use the definition of partial derivatives as limits to find f(x, y) and fy(x, y). f(x, y) = 6xy2 - 6...

A: Consider the function: fx,y=6xy2-6x3y To calculate partial derivatives with respect to “x” using the...

Q: Differentiate the following and simplify the answer to the simplest form￼

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Q: Find the rate of change of y with respect to x when x=3000 and y=100

A: Given data: The given expression of the function is 180x0.75y0.25=230,734. The given value of unit...

Q: A = 2a, + 4a, + 10a, and B = - 5a, За, %3D

A: Part (a) At point P(0,2,-5). ρ=x2+y2+z2=0+4+25=29 ϕ=tan-1yx=tan-1(∞)=π2 Transform the vector -5az+...

Q: Find the point that is located on the graph of each of the following equations: y =X y = x2 y = (x- ...

A: To find the point that is located on the given equation, we choose some arbitrary value of x and sub...

Q: The question is attached

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Q: question is in picture below

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Q: A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The...

A: Given: (a). The sterilization tank contains 80 gallons of a solution of 4% ordinary household bleach...

Q: (1) Consider the following: x = 1+t-1 and y = t2. Express in the form y = f(x) by eliminating the p...

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Q: Find the vertical asymptotes, if any, and the value of x corresponding to holes, if any, of the grap...

A: for the vertical asymptote of the given rational function, we equal denominator with zero.x²−81=0⇒x=...

Q: An irrigation system uses a straight sprinkler pipe r = 500 ft long that pivots around a central poi...

A: Area of a section of circle = R22θ Where θ is a subtended angle in radians, R is the radius.

Q: The unit circle that follows has been divided into twelve equal arcs, corresponding to t-values of 0...

A: The unit circle that follows has been divided into twelve equal arcs, corresponding to t-values of 0...

Q: Find the points on the curve y= 2x3 +3x2 -12x +1where the tangent is horizontal.

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Q: Find the derivative. g(x) = (4x – 2)° – Vr + 8

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Q: The question is attached

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Q: d a² – 2x Find dx

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Q: Consider the four petaled rose r = sin(2θ). Find the area of one leaf, then prove that the total are...

A: Given four petaled rose r=sin(2θ). We need to find the area of one leaf. First let us sketch the cur...

Q: Find:

A: we have to find the given limit limx→-3(x+16)

Q: I need help with 21

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Q: 3x/4-1/3=1-2/6(x-1/8)

A: 3x4-13=1-26x-18 We need to solve the given equation.

Q: Calculus Question

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Q: Question 10. The curve r(s) = (s,3 cos , 3 sin ) is parameterized by arc length. Find the Frenet-Ser...

A: The curve, r(s)=<45s,3coss5,3sins5> The Frenet-Serret frame {T,N,B} for r(s) are given by, The...

Q: Find the following limit:

A: To Determine: Find the following limit. Given: we have limx→53x-7 Explanation: we will find the limi...

Q: Use vectors to prove that a parallelogram is a rectangle if and only if its diagonals are equal in l...

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Q: Need help with this math problem. Thank you!

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Q: The figure shows graphs of r', the rate of change of revenue, and c', the rate of change of costs (b...

A: A profit is given by the revenue cost. The rate change of curves r' and c' are given, So the rate wo...