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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answ...

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Q: In following problem, two linearly independent solutions and are given to the associated homogeneous...

A: Given x2y" + 2xy' - 2y = x2 , y1 = x-2, y2 = x

Q: Let h(x)=f(x)*g(x), and k(x)=f(x)/g(x). Use the figures below to find the exact values of the indica...

A: Given To find h'(0) and k'(-2)

Q: Pkert (K-P)+PgeTt 15. Consider a function P defined by P(t) =-rperi, where Po, K and r are positve c...

A: Given function is P(t)=P0Kert(k-P0)+P0ert where P0,K,r are positive constant. Since r is positive co...

Q: #42

A: The number of children's enrolled E(in thousands) is given by, E(t)=21892-2812.9t1-0.2759t. Where t ...

Q: Evaluate gradø if 9= log(x² + y² +z')

A: Consider that the gradient of a scalar function ∅x,y,z is given by, grad ∅ =i^∂∅∂x+j^∂∅∂y+ k^∂∅∂z Su...

Q: 6. Check whether lim f(x) exists or not, where f (x) is defined as follows. x→-1 5x + 3, x<-1 f(x) =...

A: Given: fx={x3+5, x≥-15x+3, x<-1

Q: If f(x) = |x|, then f(−1) = 1 and f(3) = 3 butf(x) is never equal to f(3) − f(−1)/3 − (−1)=1/2. Whyd...

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Q: Divide the first polynomial by the second. State the quotient and the remainder.x3-3x2-20x+12 x...

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Q: #12)

A: P=$4,000 , r=8%=0.08 Now by using compound interest formula for continuously compounding, we have A=...

Q: Evaluate algebraic expression for the givenvalue or values of the variable(s). 2x + y/xy - 2x, for x...

A: Given: fx,y=2x+yxy-2x for finding value of function at given point we put x=-2, y=4 in given express...

Q: Given y = V4x + 5, find the differential dy when a = 7 and dæ = 0.3. %3| Round your answer to three ...

A: Given data: The expression for the given function is y=(4x+5)1/2. The given value of x is x=7. The...

Q: sum & difference identities, condense each of t 1. cos25 cos15° – sin25°sin 15° 3. sin140°cos50° - c...

A: Solution :-

Q: Convert the angle π/2 in radians to degrees.

A: We have to convert angle π2 radian to degrees. we know that 1 radian=180π degree To convert radian ...

Q: 3245 2245z+8 2z+5 gʻ(z) = 224 5z+8

A: Given that: The equation g(x) = ln x2 + 5x + 8x3 + 5x + 8 .

Q: Find the orthogonal trajectories for the family of curves y2 = Cx3 . Use a graphing utility to graph...

A: Given curve is y2=Cx3.

Q: Calculus Question

A: Given: y'+4y=128x

Q: What is the first derivative of f(x) = ln 3z²+7z ?

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Q: All boxes with a square base, an open top, and a volume of 200ft^3 have a surface area given by S...

A: We differentiate S(x) with respect to x. S(x)=x2+800xS(x)=x2+800x-1S(x)=2x-800x-2S'(x)=2x-800x2

Q: Divide using long division. State the quotient, q(x), and the remainder, r(x) : (3x2 - 2x + 5)/(x - ...

A: Given expression is 3x2-2x+5x-3.

Q: Differentiate x3 + 2x2 + 5x + 9

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Q: Use transformations of f(x) = 1/x or f(x) = 1/x2 to graph the rational function: g(x) =1/(x + 2)2

A: To determine: Graph of g(x)=1x+22 using graph of f(x)=1x or f(x)=1x2

Q: Please show the steps to get the answer

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Q: In algebra, the result of the division shown below can be written x +2x +1%3D(x-3)• (D x+5 x-3x²+2x+...

A: Given,

Q: Psychology: learning. A mathematical model for the aver- age of a group of people learning to type i...

A: A mathematical model for the avg of a group of people learning to type is given by ...

Q: . What is the average rate of change of the function g(t) over the interval from t=atot=b? How is it...

A: Suppose gt be a function defined on the interval a , b Then, the average rate of change of the funct...

Q: If f' (2) = 6, and g(x) = 4f(x), what is g'(2)? Do not include "g'(2) =" in your answer. For example...

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Q: Find the limits

A: We have to evaluate limx→9x-3x-9 . If we put the limit then we can see that it is 00 form, therefore...

Q: Absolute maxima and minima Find the absolute maximum and minimum values of the following functions o...

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Q: Sketch the solid whose volume is given by the integral and evaluate the integral.

A: Given:∫π23π2∫03∫r29 r dz dr dθ=∫π23π2∫r29 z03 r dr dθ=∫π23π2∫r29 3 r dr dθ=3∫π23π2 r22r29 dθ=32∫π23...

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. LaSV dz dy For cla...

A: The given integral is: ∫-22∫-4-y24-y2dxdy The cartesian coordinates are given by x, y and polar car...

Q: By about how much will ƒ(x, y, z) = ln√(x2 + y2 + z2) change if the point P(x, y, z) moves from P0(3...

A: The given function is, fx,y,z=lnx2+y2+z2 distance ds=0.1 unit in the direction of 3i+6j-2k

Q: Solve the equation on the interval 0<0<2x. cot 0 + V3 = csc 0 %3D

A: cotθ+3=cscθ On simplification, we get cosθsinθ+3=1sinθ⇒cosθ+3sinθsinθ=1sinθ⇒cosθ+3sinθ=1⇒12·cosθ+32·...

Q: Please how me how to do section b.

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Q: Evaluate the integrals in ∫ln x dx/x√(ln2 x + 1)

A: Consider the following integral: ∫lnxxln2x+1dx=I Substitute ln2x+1=u→2lnxxdx=du in the above integra...

Q: 8. Evaluate (-3t-2/3 – 4) dt. Enter your answer as an exact fraction if necessary.

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Q: Find an equation of the tangent line to the curve y= 10xat the point (1, 10).

A: Given: y=10x for finding tangent of given curve at given point we need slope m of tangent at given p...