In the quadratic equation Ax2+ Bx + C=0 describe the roots when 32 -4AC is negative. The roots are real and distinct. The roots are complex conjugates. The roots are real and equal. O The roots are complex and equal.

Q: Consider the function f : R → Rj, f(1) = (x – 4)°. Complete the following: fis because the equation ...

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Q: dy 4. ST 81–16y²

A: As per our guidelines we are supposed to answer only one question 

Q: Find the general solution to the differential equation. y' = 6xy2 y

A: The given differential equation,         y'=6xy2

Q: Evaluate the following integrals. Express the final answer in its simplest form and without negative...

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Q: Given f(x,y) = x3y-3xy³. Evaluate fdy O 14y-27y + C 6. O -6y³ +8y/3+ C бх2 - O 6x2 – 45x + C 4 2x2 –...

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Q: For the function y =f(x), it was found out that f(c) = 0. What can be said that x=c ? critical point...

A: topic - functions

Q: 11. The maximum point of the curve * y =r' - 3r° + 4 is at

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Q: Let f(-6) = -5 and f'(-6) = 7. Then the equation of the tangent line to the graph of y= f(x) at r = ...

A: Given query is to find the equation of the tangent.

Q: What is the equation in standard form of a hyperbola with center C(- 1, – 3), a focus at and a verte...

A: In this case transverse axis is y axis.

Q: 12-41-12 dx Evaluate the integral: I+2

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Q: A parametric representation of the curve of intersection of the two surfaces x2 + 5y2 - z = 0 and z ...

A: The given curves are: x2+5y2-z=0 & z=4y2+36 ⇒x2+5y2-(36+4y2)=0⇒x2+y2-36=0⇒x2+y2=36

Q: Write the equation of the line tangent to the graph of r = 5 cos (40) when 0

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Q: Determine the present value P that must be invested to have the future value A at simple interest ra...

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Q: Which of the following is the approximate value of e' if polynomial expansion P(x) centered at a = 0...

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Q: Find the taylor polynomials of orders n = 0,1,2,3, and 4 about x=x0, and then find the nth Taylor po...

A: Given : taylor polynomials of orders n = 0,1,2,3, and 4 about x=x0, Pn(x) for the function in sigma ...

Q: Find y" il y= (r+ 1)² + VE when t= 1. O a.1.75 Ob.3.5 Oc.225 Od.2.25

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Q: Find dy/dx. No need to simplify. With explanation

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Q: Let W = F(x , y, z) = xy + yz + xz , where x(t) = 3 + sin(2t -4), y(t) = t2 and %3D dW z(t) = 3 - t....

A: Derivative using product rule

Q: CALO2- INTEGRAL CALULUS INTEGRALS OF TRIGOMOMETRIC FUNCTI ONS HTE GRATE Hも FO110WIN の 5) (xcot (10x?...

A: A detailed solution is given below

Q: a. Find the local extrema of the function f(x) = 3 cos 4x + sin 4x on the interval 0 sxs and say whe...

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Q: Find the limits of the functions below a) limr-3 x* sin x b) lim,

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Q: 2n a. Find the local extrema of the function f(x) = cos 3x + 3 sin 3x on the interval 0sxs and say w...

A: 0≤x≤2π30≤3x≤2πf(x) = cos 3x +3 sin 3xf'(x) = -3 sin 3x + 33 cos 3x f'(x) = 0-3 sin 3x + 33 cos 3x=0t...

Q: y = x²(x – 5)²

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Q: whether the geom 08. (-7)" – 1 Σ 8" n = 1

A: Solution is given below:

Q: 1. The product of two numbers is 24. Find the numbers if (a) the sum of the two numbers is minimum, ...

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Q: The area between y = n + x* and the x- axis in the interval [0, 1] approximated using left endpoint ...

A: Find your answer below 

Q: 4 3 2 1 -2 -i -1 -2 -3 What is the equation in general form of the hyperbola whose graph is given ab...

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Q: Assembling a jigsaw puzzle. Combination O Permutation

A: The jigsaw puzzle is about the arrangement where position and orientation matter. Thus, the correct ...

Q: Eight workers are assigned to 8 different jobs. Combination Not Combination

A: Eight workers are assigned to 8 different jobs. We have to determine whether it is combination or no...

Q: [25/² – 36 dz Evaluate the integral: (A) Which trig substitution is correct for this intearal?

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Q: Evaluate: Il2dxdy using inner limits 0 to y and outer limits 1 to 2. O a. 0.71 O b.0.375 Ос. 3.75 d....

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Q: ne region bounded by f(x) = - 1x + 7x + 18, = 0, and y O is rotated about the y-a ne volume of the s...

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Q: Write the first five terms of the recursively defined sequence. a1 =6, ak+ 1 %3D %3D a2 = 23 = a4 a5...

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Q: Determine convergence or divergence by any method. Š (-1)"n n=0 Vn2 +5 The series diverges, since li...

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Q: Write in radical form. Do not simplify. ーxー7/6 Need Help? Read It Watch It

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Q: A depositor opens a new savings account with $5000 at 8% compounded semiannually. At the beginning o...

A: Let's find. 

Q: 5. Consider the graph of y = 7-3x2. Calculate the area enclosed by the curve y= 7- 3x and the x-axis...

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Q: Write a chain rule formula for the following derivative. aw for w = f(x, y, z); x = g(r, s, t), y = ...

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Q: The length of an arc of a polar curve r = f(0), a < 0 < b, is given by the formula: %3D Find the len...

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Q: Find the equation of the tangent line to y = arctan(2x) when x = V3 O y - = ( - ) 1 3 O y - = }(2 - ...

A: Let's find. 

Q: Find the indefinite integral: Sx(x³ + 1)dx x4 + x+c x/5 + x2/2 + c x5 + x2 + c O 5x5 + 2x2 + c

A: Find the indefinite integral

Q: Find the derivative of sin In x O sin(Inx)/x cos(Inx)/x O cos(1/x) O sin (1/x)

A: topic - derivative of a function

Q: The Normal component of the acceleration of a moving object in space at time t is given by aN + 1 If...

A: Explained below

Q: Find the radius of convergence and the interval of convergence. EA (* + 6)* k=0 Radius of convergenc...

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Q: Evaluate the following limits 5 a) limx-0- 5 5 b) limx-o+ 5 c) limx-0 x3

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Q: The region bounded by f(x) = - 4x2 + 20x + 96, x = 0, and y = 0 is rotated about the y-axis. Find %3...

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Q: Solve the problem. Find the area of the triangle determined by the points P(-3, 6, -4), Q( 2, 10, -9...

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Q: petermine if the improper integral ex J dx is convergert or diverg unt. If it is convergent, detumin...

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Q: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx)  y = 6u3,u = 7x ...

A: To find dydx bu using Leibniz's notation for the chain rule: dydx=dydududxy=6u3, u=7x-4    

Q: A space probe in the shape of the ellipsoid 16x +y + 4z = 20 enters a planet's atmosphere and its su...

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