In Exercises 81-83, perform the indicated operations and write the result in standard form. 1 +i 1 -i 8 83. 4 81. (2 + i)(3 – i) 82. 1 + 2i 1 - 2i 1 + i

Q: Find the areas of the surfaces generated by revolving the curves about the indicated axes. If you ha...

A: Area under the curve fx=24-x12 on interval 0, 154:The area under a curve is the area between a curve...

Q: Compute f 1 (x) and find an equation of the tangent line to the graph at x = a. f (x) = x4 , a = 2

A: Consider the given function fx=x4  When x=2, then y=fx=24=16 Hence, point on the curve is 2, 16   To...

Q: If the profit function for a product is P(x) = 2800x + 85x2 − x3 − 109,000 dollars, selling how many...

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Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: The general form of quadratic equation is  Ax2+Bxy+Cy2+Dx+Ey+F=0, B≠0 The angle is  cot2θ=A-CB The r...

Q: find the derivative of y with respect to x, t, or u,as appropriate. y = ln (sec u + tan u)

A: Given:             y=lnsec u+tan u The derivative of y with respect to x,            ddxy=ddxlnsec u...

Q: Evaluate the limit if it exists. If not, determine whether the one-sided limits exist. For limits th...

A: limθ→π2θ secθ Now the left hand limit at θ=π2 is, limθ→π2-θ secθ=limθ→π2-θcosθ=∞ & the right han...

Q: For Exercises 32-34, determine whether the sequence is geometric. If so, find the value of r. 3 3 32...

A: The sequence in which each term is a constant multiple of the previous terms can be termed as Geomet...

Q: 9. Find all x where the tangent line to y = f(x) = sin° (x) – sin(x) is horizontal.

A: Given,          The tangent line y=fx=13sin3x-sinx is horizontal.

Q: In Problem,find the domain of each rational function.

A: Given: Rx=xx3-8 To Find: The domain of the given rational function.  

Q: find the inderinite integral it 2. dx 7-3x3

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Q: indefinite integral of this   complete solution

A: the given indefinite integral is: ∫x2x3-14dx we have to evaluate the given integral and show that th...

Q: Write and solve the system of linear equations described by the application and then answer the ques...

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Q: Evaluate the limit if it exists. If not, determine whether the one-sided limits exist. For limits th...

A: A limit exists at a point if the left hand limit equals the right hand limit. For the expression [x]...

Q: Put the equation in standard form and find the hyperbola’s asymptotes. Then sketch the hyperbola. In...

A: The simplification of the given equation helps to convert it into the standard form of hyperbola. T...

Q: Choose True if the statement is correct, otherwise False. Any function y = f(x) can be expressed as ...

A:   To state true or false.

Q: Show that the number 4p is the width of the parabola x2 = 4py (p > 0) at the focus by showing tha...

A: The parabola x2=4py where p>0 represents a vertical parabola with the y-axis as the axis of symme...

Q: In the given question as follows , find the nth Maclaurin polynomial for the function:- f (x) = x2e-...

A: Maclaurin series is a special case of Taylor's series where the specific point on which the series i...

Q: Candy The following data represent the weight (in grams) of various candy bars and the corresponding...

A: (a).            A scatter diagram for the following data :                     (b).          Answer ...

Q: The motion of a particle in space is defined by the parametric equationx(t) = −t2 + 3t + 1, in meter...

A: Given: x(t)=-t2+3t+1  in meter y(t)=2t+5 in meter  

Q: Prove that  lim x→4 x2 =  4. 2

A: R. H. L. limx→4+ x2= 4 2= 16 L. H. L. limx→4- x2= 4 2= 16L.H.L.= R. H. L.

Q: Give equations for ellipses. Put each equation in standard form. Then sketch the ellipse. Include th...

A: Given equation of an ellipse 169x2+25y2=4225. To put the equation in standard form and sketch the el...

Q: Find dy/dx and d²y/dx². x = t? + 1, y = t? + 5t (2t + 5) dy dx 2t dy dx2 (21(2) – (2t + 5)(2)) 4? 2t...

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Q: Show that the minimum distance from the origin to a point on the plane ax + by + cz = d is |d| Ja? +...

A: Given :               ax + by + cz = d         We know that minimum distance (p) of a point x1,y1,z1...

Q: Use implicit differentiation to find dy/dx

A: ddxarcsinx2+y2=11-x2+y22ddxx2+y2=11-x2+y22·x+yddxyx2+y2=x+yddxy1-x2-y2x2+y2

Q: The hyperbola (y2/4) - (x2/5) = 1 is shifted 2 units down to generate the hyperbola ( y + 2)^2/4 - x...

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Q: Describe the tangent line at an arbitrary point on the graph of y = 2x + 8

A: we have to describe the tangent line at an arbitrary point on the graph of y=2x+8  

Q: Use Taylor series you already know to find the Taylor series generated by f(x) = x° sin(2x) at x = 0...

A: Proceed as shown below...

Q: Define g(t) = (1 + 21/t) -1 for t ≠ 0. How should g(0) be defined to make g left-continuous at t = 0...

A: Here given function as gt=1+21t-1or gt=11+21t Consider g(x) is left continuous at x=0 Thus limt→0-gt...

Q: Choose (a) or (b). The derivative at a point does not exist if the tangent line at that point is ( a...

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Q: Vx²+3 3. lim

A: Here limit is present in infinite by Infinite indeterminant form.

Q: Find the radius of convergence for the following series

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Q: 「xytス

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Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: Definition and methods help to find the required limit of the given function. A value is said to be...

Q: solve

A: Given : The limit , limx→0 1x sin x - 1x2    

Q: Evaluate the limit if it exists. If not, determine whether the one-sided limits exist. For limits th...

A: We have to find the limit: limx→1x3-xx-1 This is 00 indeterminate form so simplifying the limit, lim...

Q: Find the volume of the solid above the region D={(x,y) : 0< xs V27, 0s ys 27-x2} and between the pla...

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Q: Evaluate the following sum. -4+5+14+23+32+ .. +176

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Q: Find an approximation of the area of the region R under the graph of the function f on the interval ...

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Q: Show that the curve x = 2 cos(t), y = 3 sin(t) cos(t) has two tangents at (0, 0) and find their equa...

A: Given that      x = 2 cos(t)  , y = 3sin(t)cos(t) Here we have to show that these curves have two ta...

Q: In the givn equation as folows ,  state where the power series is centered:-

A: Given: ∑n=1∞-1n2n-12nn!xn Concept Used: Consider a power series ∑n=1∞anx-an Here 'a' is the center o...

Q: Write as a single integral in the form f(x) dx. f(x) dx FXx) dx - Ax) dx + -3 f(x) dx

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Q: A firm can produce 100 units per week. If its total cost function is C = 600 + 1400x dollars and its...

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Q: Identify the graph of each equation without completing the squares.

A: To identify the graph of equation 2x2+2y2-8x+8y=0

Q: Given the graph of the functionƒ(x) below, use a left Riemann sum with 4 rectangles to approximate t...

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Q: Solve the triangle, if possible. 35.1 27 21 B. Select the correct choice below and, if necessary, fi...

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Q: An airplane is heading N35°E at a speed of 460 mph.  A 75 mph wind blows from the southwest at an an...

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Q: Describe the regions defined by the inequalities and pairs of inequalities.x2 + y2 &gt;1, x2 + y2 &l...

A: Describe the regions defined by pair of inequalities. x2+y2&gt;1 and x2+y2&lt;4. The equation x2+y2=...

Q: What is the result of completing the square for f(x) = x 2 + 1?

A: To Complete the square  of f(x)=x2+1

Q: If the total cost function for a product is  C(x) = 150(0.02x + 6)3 dollars,  where x represents the...

A: Now , we will find the minimum average cost per hundred units .

Q: Use the limit definition to compute f' (a) and find an equation of the tangent line. f(t) = √(t2 + 1...

A: Consider the provided function, ft=t2+1    a=3 Find the limit by the definition to evaluate  f'a and...