Use the graphing utility to graph the curves x = 4y² and x = = 4√//y.

Q: Given that  lim x→2 f(x) = 1    lim x→2 g(x) = −4    lim x→2 h(x) = 0, find the limits, if they…

A: According to bartleby guidelines we are supposed to do only three subparts. If you want to solve…

Q: Find the unit tangent vector to the curve defined by r(t) = (4 cos(t), 4 sin(t), 5 sin²(t)) at t - 7…

A: Solution is given below:

Q: 5. Find the values of x where the graph of the function has a point of inflection. Given: f(x) = x4…

A: We need to find inflection point.

Q: Let f(x) = 3√x If g(x) is the graph of f(x) shifted up 4 units and right 1 units, write a formula…

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Q: You are designing a 500 cm³ right circular cylindrical can whose manufacture will take waste into…

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Q: Find the volume of a solid obtained by rotating the region under the graph of the function f(x) = 27…

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Q: Evaluate lim f(x) and lim f(x) for the following function. Use ∞o or -∞o where appropriate. Then…

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Q: Find the arc length of the curve below on the given interval. 3 1/3 4 y= 2x5/3. - +7 on [1,8]

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Q: For the function f whose graph is shown, state the following. (If the limit is infinite, enter 'o'…

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Q: sec²x. - y X |dx +N(x,y) dy=0 dx

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Q: Qu Solve the following ordinary differential equations:

A: dydx+1xy=xy3divide y3  both sides 1y3dydx+1x×1y2=x

Q: 2 Let f(x) = x² - 6x - x + 30 and g(x) = 16 - x². a. Graph these functions on the same set of axes.

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Q: B) At what value(s) of x does the graph of g(x) have relative minimum(s)? Justify y

A: here , we  have graph of a function g' (x)  , derivative of a function g(x)  over the interval x…

Q: The sketch (and shading) of the region bounded by the graphs of the algebraic functions y₁ = x² − 9…

A: Consider the region bounded by the graphs  y1=x2-9y2=-x+4 and the vertical lines x=0 and x=2

Q: The cost function for manufacturing electric drills is estimated to be: C(x): 4x². = - 6x + 784.…

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Q: Use the definition of continuity and the properties of limits to show that the function is…

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Q: Determine the graph of the equation x2+y2−z2=100.  Choose the correct graph of the equation.

A: We need to determine the graph of the equation given by : x2+y2-z2=100

Q: 5s - 7 (s + 3) (s² + 2)

A: Since we are given with multiple numbers of questions and answer will be according to the guidelines

Q: Use algebra and limit laws to find the following limit if it exists. If it does not exist, explain…

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Q: Find the arclength of y = 2x³/2 on 1 ≤ x ≤3

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Q: The owner of a skating rink rents the rink for parties at $1200 if 60 or fewer skaters attend, so…

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Q: Find the a. v. u, |v|, |u| b. the cosine of the angle between v and u c. the scalar component of u…

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Q: Q₂: Find the general solution for the below differential equations (using undetermined coefficients…

A: A complete solution is given below.

Q: M(x,y) dx + (y³ + x2y + x) dy = 0

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Q: By determining f'(x) = lim h→0 f(x) = 6x² = f(x+h)-f(x) h (Simplify your answer.) find f'(4) for the…

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Q: Use the washer method to find the volume of the solid generated by revolving the shaded region about…

A: Given curves y=1 ,y=cosx ,-π3≤x≤π3

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: f(x) X 1) Given the graph of f(x) above, use geometry to evaluate each of the following parts below.…

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Q: 10. The approximate length, L, of rope in a ball of rope is given by the formula 4 = 4R³ 3², where R…

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Q: (siny-2ye¯*sinx) dx + (cosy + 2e-*cosx) dy = = 0

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Q: Use a CAS to plot the surface. Identify the type of quadric surface from your graph. 2 X 16 1= Z 25…

A: The surface is given as , x216-1=y225+z23 Plot the surface.

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) √3- t lim t-0 3 +t- t

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Q: 24. n³ +5n is divisible by 6;

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Q: An oil retinery produces oil at a variable rate given by the following equation, where t is measured…

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Q: Given that vector u has length 2, vector v has length 3, and the dot product of u and v is 1, what…

A: We need to find the value of 2u-v

Q: 1. Find the general solution for the following differential equation. a. y'= 2y - 4x

A: You have posted multiple question which are not interlinked and i can solve only one question as per…

Q: 2(x³ + xy² + y)dx + (2x²y³ + 4xy² + 2x²y + x^y + 2x)dy=0; y(2) = 0

A: Let's solve given differential equation.

Q: Find the point-slope equation of the plane passing through the point (-14, 7, -2) and having x-slope…

A: A detailed solution is given below.

Q: Given f(x, y) = 6x² fx (2, 3) = fy(2,3)= - 5xy + y, find the following numerical values:

A: f(x,y)=6x4-5xy2+y5fx(x,y)=∂ ∂x(f(x,y))fy(x,y)=∂ ∂y(f(x,y))we know  ∂ ∂x(xn)=nxn-1

Q: The function h(x) defined as: = 1 x+7 can be expressed in the form f(g(x)) where g(x) = (x + 7) and…

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Q: 2 (e^)² = e²x why rather than (e^)² = etz 2

A: To find the integral.

Q: ind the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A: To find the volume of the reagion

Q: you

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Q: Select the law which shows that the two propositions are logically equivalent. (¬p^ (rv¬q)) v (…

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Q: A car rental agency charges $100 per week plus $0.10 per mile to rent a car. a. Write an equation…

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Q: Let f be a twice-differentiable function with domain R. 3 [²³ f We also have the following table: We…

A: I = ∫13 f''(x) x2dx I =[(x2)∫f''(x)dx]13 - ∫13{ ddx(x2)∫f''(x)dx}dxI =[(x2)f'(x)]13 - ∫132x…

Q: Determine the value of lim f(x) x →1 when f satisfies the inequalities 8x ≤ f(x) ≤ x³ +5x+2 on [0,…

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Q: lim sin4x / x x—>0

A: To evaluate the following limit. limx→0 sin4xx

Q: lim In X-8 1-)-e X ex

A: Given limit limx→∞ [ ln( 1x ) - ex ]

Q: 1. Evaluate | 2®sinh *(® +1)de

A: