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Q: Find the horizontal asymptote, if there is one, of the graph of the rational function: h(x) = 12x3/(...

A: Given function is h(x)=12x33x2+1

Q: Differentiate the function   f(x) = x ln x -x

A: Given: fx=xlnx-x

Q: Use a CAS to plot the implicitly defined level surfaces x + y2 - 3z2 = 1

A: The given function is

Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to ...

A: To evaluate the second derivative of the function at the given point (0,3). f(x)=9x+9

Q: An arithmetic sequence is a sequence in which the___between successive terms is constant.

A:   An arithmetic sequence is a sequence in which  the difference between successive terms is constant...

Q: Find the values of x for which the series converges.

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: a.Find the solution of the given initial value problem in explicit form. b.Plot the graph of the sol...

A: Divide differential equation with y2 to get classic separable equation.  This is permissible for all...

Q: graph the function and find its average value overthe given interval. g(x) = | x | - 1 on a. [-1, 1]...

A: gx=x-1 The graph is,

Q: The greatest integer function, also known as the floor function, isdefined by [ x ] = n, where n is ...

A: Consider the given function, y=x draw the table of points, x y 0<x<1 0 1<x<2 1 ...

Q: Find the numeric value ( in terms of c ) for the following definite integral analytically by (a) Int...

A:

Q: Solve the system.

A: Given

Q: a. Verify the differentiation that the formula is correct dx a2Va²-x² + C 3 (Va2-x²)

A: to verify the result

Q: Find the limits by rewriting the fractions first.

A: We have to find the limit: limx, y→0, 01-cosxyxy Rewriting the fraction using trigonometric formula,...

Q: Determine the following limits at infinity. 10 lim a5 + *+

A: Given, limx→∞a5+1x+10x2b

Q: Solve compound inequality. 6 <x + 3 < 8

A: The given inequality is 6<x+3<8.  

Q: 8- what is average value of f(x)= |sinx| between 3pi/2 and 7pi/3

A: The given function is  f(x) = |sinx| Interval is given as 3pi/2 to 7pi/3

Q: Find the three cube roots of 27. Write roots in rectangular form.

A: Find the three cube roots of 27                      27=27cos 0°+isin 0°zk=273cos0°+360°.k3+isin0°+3...

Q: The graph of y = A sin Bx has amplitude =_____ and period =______.

A: We have to fill in the blanks: The graph of y=A sin Bx has amplitude =_____ and period =______. We k...

Q: Graph: f(x) = 3x

A: Concept;   The calculus helps in understanding the changes between values that are related by a func...

Q: Use a graphing utility to graph the equation: x2 + 4xy + 4y2 + 10√5x - 9 = 0

A: we have been given the equation   x2 + 4xy + 4y2 + 10√5x - 9 = 0

Q: solve the given differential equation on the interval x > 0. Use the variation-of-parameters tech...

A: To Solve: x2y''-3xy'-12y=x4+5x2, x>0. Explanation: x2y''-3xy'-12y=x4+5x2.....iFirstly, we will fi...

Q: Find the limit. Use l’Hospital’s Rule where appropriate.If there is a more elementary method, consid...

A:   Find the limit. Use l’Hospital’s Rule where appropriate.If there is a more elementary method, cons...

Q: Define Higher order Derivatives ?

A: To define: Higher Order Derivatives

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the ...

A: Given data: The given function is f(x,y,z)=2ln(xy)+2ln(yz)+2ln(xz). The given point is P0(1,1,1). Th...

Q: 1. The ground crew is filling the fuel tanks. You know they fill the tanks at a rate of r=100et, whe...

A:

Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.Express the argument as a...

A: Given, z1=2+2iz2=1+i

Q: Find an equation of the normal line to y = x2 at the point (2, 4). (The normal line at a point is pe...

A: y=x2 Differentiating with respect to x, we get dydx=2x Now slope of the tangent line at 2, 4 is, dyd...

Q: Solve ,  y" - 14y' -32y = 0

A: We have to solve  y" - 14y' - 32y = 0  (D2 - 14D - 32)y = 0 The auxiliary equation is  m2 - 14m - 32...

Q: Determine whether the statement is true or false. If the statement is false, make the necessary chan...

A: Consider the statement x3 − 64 = x + 4(x2 + 4x − 16)  

Q: Find the limit. Use l’Hospital’s Rule where appropriate.If there is a more elementary method, consid...

A: Solution:-  we have to solve, y=limx→∞x tan(1x)

Q: Use a computer algebra system to evaluate theintegral. Compare the answer with the result of using t...

A: Given: I=∫cosec5xdx we know that ∫cosecnxdx=n-2n-1∫cosecn-2xdx-cotxcosecn-2xn-1                     ...

Q: Write the complex number 20(cos 205° + i sin 205°) in rectangular form. If necessary, round to the n...

A: Our Aim is to write the complex number 20[cos(205°)  + i sin(205° )] -(i)in rectangular form.

Q: For the point with the given polar coordinates (4, 135°), determine the quadrant ________ in which t...

A: Let the polar coordinates be = r, θLet the rectangular coordinates be = x, yGiven that - r, θ = 4, 1...

Q: sketch the shifted exponential curves y = 2x - 1 and y = 2-x - 1

A: The given exponential curves are:

Q: What are the derivatives of the six basic hyperbolic functions? What are the corresponding integral ...

A: Derivatives of the six basic hyperbolic functions: dsinhxdx=coshxdcoshxdx=sinhxdtanhxdx=sech2xdsechx...