In Exercises 65-72, find an equation of the form X = z2

Q: Find an equation of the tangent plane to the surface z = √(9 − x2 − y2), at the given point (1, 2, 2...

A: The surface given is Fx,y,z=√(9 -x2 -y2) -z =0. The derivative of the surface coordinates with respe...

Q: Use your graphing utility to graph each side of the equation 3x = 2x + 3 in the same viewing rectang...

A: Use your graphing utility to graph each side of the equation 3x = 2x + 3 in the same viewing rectang...

Q: Find the limit.

A: Let the given limit be L - L = limx→∞ xtan1x            .............(1)L = limx→∞ xtan1x1x×1xL = li...

Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain...

A: Given that f and g are two continuous functions on [a, b].  

Q: Verify the identity: (sin 2x + sin 6x)/(sin 2x - sin 6x) = -tan 4x cot 2x

A: We have to verify the identity: sin 2x+sin 6xsin 2x-sin 6x=-tan 4x cot 2x We know the sum and differ...

Q: For the following parametric equation x(t) = tan t and y(t) = sect find the %3! %3D d²y angent line ...

A: Explanation of the solution is given below...

Q: Determine the possible points of discontinuity of the following functions and the type of discontinu...

A: Given function      f(x)=x2-4x-2=(x+2)(x-2)x-2=x+2    if x≠2,-4                                     ...

Q: A pile of sand is in the form of a right circular cone of altitude 7 feet and slant height 25 feet. ...

A: Given  The right circular cone  altitude 7 feet and slant height 25 feet . The sand weighs 107.5 lb ...

Q: Approximate the area between f(x) = x+2 and the x-axis from x 1 to x 7 using a trapezoidal sum with ...

A: fx=x2+2,  x=1 ,  x=7,  n=3. Here, h=b-an⇒h=7-13⇒h=2 Therefore the subintervals is, 1, 3, 3, 5, 5, 7 ...

Q: In Exercises 7-12, compute the derivative. 7. r( t) = ( t, t 2 , t 3 )

A: Given: r(t)=t, t2, t3 To determine: Derivative of given vector

Q: NOTE: Solve this as soon as possible, I need this urgently. If tangent lines to the ellipse 9x² + 4y...

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Q: Determine a rational number that is located between -2 ¼ and -2.8.Justify that the point is located ...

A: The given two rational numbers are  -214 and  - 2.8

Q: write the partial fraction decomposition of the rational expression: (2x2 - 18x - 12)/(x3 - 4x)

A: We have to write in partial fraction decomposition of the rational expression: 2x2-18x-12x3-4x Rewri...

Q: A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed,...

A: Given data: Mean life of tire is m=29000 miles. Standard deviation is σ=2200 miles. Percent of tire...

Q: 2. 4 9. 10 11 12 13 x -1+ 2- -3+ -4+ -5 6- (2,-6) (12,-6) The graph of y = f(x) consists of a semici...

A: Giveny=fx consists of semicircle with end points 2,−6 and 12,−6To find∫212fxdx

Q: (a) As dry air moves upward, it expands and cools. If the ground temperature is 20 Cand the tempera...

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Q: a) Só xv4 - x2 dx

A: Since you have asked multiple questions in a single request so we will be answering only first quest...

Q: What is the common ratio in a geometric sequence?

A: we have to tell what is the common ratio in a geometric sequence.  

Q: Answer the question in the image.

A: Given that y=10-6x+x2, y=-10+6x-x2,x=1 and x=5 about the line y=8 find the volume of the solid  

Q: Given that 6g(x) + xsin(g(x)) = 10x2 - 9x - 9 and g((3)/(2)) - 0, g' ((3)/(2)). g'((3(/(2)) =

A: Given that, 6g(x) + x sin(g(x)) = 10x2 - 9x - 9 Differentiating above with respect to x we get, 6 . ...

Q: Evaluate the question below

A:

Q: Determine the following indefinite integral. Check your work by differentiation.

A: Given: I=∫(sec2x−1)dx

Q: Suppose that Eaz = -5 and b = 6. Find the values of %3D k= 3a c. (a + b) a. b. k=1 d. (az - bi) k=1 ...

A: We have given: ∑k=1nak=-5 and ∑k=1nbk=6. (a). To find ∑3k=1nak. Property of sigma is: ∑k=1ncan=c∑k=1...

Q: Domains of functions of three or more variables Find the domain of the following functions. If possi...

A: Given,           F(x,y,z)=y-z2   We have to find domain of above function.  We know that, The domain...

Q: 5iV3

A: The expression given is -75 is,  Simplifying the given expression ,  -75=5×5×3 ·-1. The value of -1 ...

Q: What is the Integral Test? What is the reasoning behind it? Give an example of its use.

A: The integral test: Suppose that the function fx is continuous, positive and decreasing on the interv...

Q: The figure shows a page with 1-inch margins at the top and the bottom and half-inch side margins. A ...

A: Let the length and width of the printed page be y and x, respectively. Given printed area of page is...

Q: Find the midpoint of the line segment with the given endpoints : (-2/5, 7/15) and (-2/5, -14/15)

A: Given: -25,715 and -25,-1415

Q: Suppose a, andb are series with positive terms and p. is known to be divergent. (a) If a, > b, for a...

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Q: Please help me as soon as possgible

A:

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

A: the given complex number are: z1=cos 70°+i sin 70°z2=cos 230°+i sin 230° we have to find the quotien...

Q: 04 Evaluate the following integrals; a) S xv4- x dx sine de b) S we2wdw c) S XV cos20-3cose+2

A: These are definite and indefinite integration problem and are solved in following steps. 

Q: Fill in the blank/s: Determine whether the sequence 4, 8, 12, 16, 20, . . . is arithmetic or geometr...

A: Given: 4,8,12,16,20.....

Q: Use logarithm rules to rewrite the quantity:Use logarithm rules to rewrite the quantity 2 ln(x2) + 3...

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Q: Contrary to popular belief, older people do not need less sleep than younger adults. However, the li...

A: Given the graph for number of awakenings of the people during night over various age. We need to fin...

Q: 1 For the following parametric equation x(t) = tan t and y(t) = sec t find the tangent line passing ...

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Q: Find area of the region enclosed by the parabolas y = 4x – x² and y = x² - 4x. %3D

A: Find area of the region enclosed by the parabolas y=4x-x2 and y=x2-4x as shown below. Sketch the reg...

Q: Use l’Hôpital’s rule to find the limits

A: Let the given limit be L - L = limx→0 x2lnsecxUsing L-hospital rule, differentiating numerator and d...

Q: (1) Consider the graph of function f(x): 14 6. -5 -4 -3 -2 Evaluate: (a) lim f(x) X4" (b) lim f(x) (...

A: Since you have posted multiple questions, as per our policy we will answer first question (first thr...

Q: Evaluate the limit, if it exists.

A: We have to find limit: limx→-414+1x4+x Since it is 00 indeterminate form so making it determinate by...

Q: 38. I| x²ydA, R=[-1,1] × [0, 2]

A: Given: ∫∫Rx2ydA , R=-1,1×0,2

Q: answer the question

A: The given differential equation is  ex+yy' = e2x-y

Q: Consider the function g(r) = arccos(In r). (a) Compute the domain and range of g(r). (b) Prove that ...

A: the given function is: gx=arccos(lnx) (a) we have to compute the domain and range of g(x). (b) we ha...

Q: Graphing a parabola of the form y = ax2 +c Graph the parabola. ソ= 2 Plot five points on the parabola...

A: To graph the parabola y=1/2x^2-5

Q: Solve the logarithmic equation log4(3x - 5) = 3

A: To Determine:  Solve the logarithmic equation. Given: we have log43x-5=3 Explanation: we know that t...

Q: Give the center and radius of the circle described by the equation x2 + y2 = 49, and graph the equat...

A: Given equation of circle is x2+y2=49. We know that standard equation of circle is: x-h2+y-k2=r2, whe...

Q: Find a plane through the points P1(1, 2, 3), P2(3, 2, 1) and perpendicular to the plane 4x - y + 2z ...

A:   Definition used -                 Directional vector passing through two points P1(a1,b1,c1) and P...

Q: 3. Find the derivative of (a) f(x) = (x+ 4 sin æ) (1 – 6 cos a), an (b) sin x g(æ) %3D 6x

A: a). Given function is fx=x+4sinx1-6cosx. To find the derivative of given function. Solution: Product...

Q: Simplify:  a. 251/2 b. 81/3

A: we have to simplify: (a) 2512 (b) 813  

Q: Find the midpoint of each line segment with the given endpoints (√18, -4) and (√2, 4)

A: We have to find midpoint of line segment where end points are given as: 18, -4 and 2, 4. We know the...