If the line r = (2-t, -2 + 13t, 8t) is the normal tangent line to the level surface axyz²by² = -14 at (2,-2,), then a + b = 4.

Q: Write a proof to justify the perpendicular bisector method of construction. A B Given: Prove: AB AC…

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Q: Use the figure to evaluate the definite integrals y = g(t) K +t 1 2 3 4 5 2 y 1 + -1 -2- +2 +3 2…

A: We can find the area under a curve between two points can be found by using a definite integral.

Q: Use your parametric equations to determine the following: Maximum height Time to land Where to…

A: Disclaimer: Since you have posted the sub multiple parts for the questions ,we will solve the first…

Q: the function f: Z × Z→Z × Z defined by the formula          f(m,n) = (4m+3n, 3m+2n) is bijective.…

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Q: Evaluate e √ √x +4-2 √√x²-16 2√x 4+4ln√√x+4-√√x−4+C B 2√x−4+2ln(√x+4-√√x-4)²+C…

A: I=∫x+4-2x2-16 dx =∫x+4-2x+4x-4 dx=∫x+4-2x+4x-4 dx Lets substitute u=x+4⇒dudx=12x+4=12u⇒2udu=dx also…

Q: Complex Numbers. 1. Evaluate the following. Express all final answers in rectangular form. a.…

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Q: Evaluate the integral B = {(x, y, z)| 0≤x≤2,-2 ≤y ≤2, 0≤z ≤3} with respect to x, y, and z, in that…

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Q: Evaluate: f 4dx 3x+2

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Q: 18 Find p. q if f f(x) dx + ³ f(x) dx = f f(x) dx. (Give your answers as whole or exact numbers.)

A: A detailed solution is given below.

Q: Find the indicated limit by using the limits [f(x, y) = g(x, y)] lim (x,y) → (a, b) Enter an exact…

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Q: If the average value of the function f(x) on [0, 3] is equal to 3 1 3/² 0 what is Select one: 0 6 O…

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Q: Question * O O O The following integral 1° (3 (3 - ex) dx is an improper integral of type II that…

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Q: Evaluate the line integral, where C is the given curve. (Round your answer to one decimal place.)…

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Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

A: From the given graph, we have to find the increasing and decreasing intervals.

Q: a. In a geometric progression the sixth term is 8 times the third term and the sum of the seventh…

A: nth term of the Geometric progression , an= arn-1. Note : As per Our Guidelines , we can solve…

Q: (ii) Find all values of k for which the integral fo (+)da converges and evaluate the integral at…

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Q: PROVE each identity. Show your work a) sin(x)sec(x) = tan(x) b) c) 2tan(x) cos(x) sin(y) = cos(x -…

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Q: 8. Analyze the graphs of f', then list all intervals where f is increasing or decreasing. f'(x), 1-…

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Q: Use the Integral Test to determine whether the series is convergent or divergent:   ∑1/n3

A: The give series is convergent...for detail...go through the solution...

Q: Evaluate the given integral by making an appropriate change of variables. J 9 X - BY DA, where R is…

A: NOTE: Refresh your page if you can't see any equations. . where R is the parallelogram enclosed by…

Q: Justify your answer. n=1 test, ratio test, root test The series onverges (converges, diverges) by…

A: To find by which test the given series converges or diverges.

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 6x3/2…

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Q: A pilot flies in a straight path for 1 hour 30 min. She then makes a course correction, heading 10…

A: topic :law of cosines

Q: Calculate the integral, assuming that fo f(x) dx = -4, ² f(x) dx = 4, ₁ f(x) dx = 11. (Use symbolic…

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Q: The graph below is the function f(x) 543 -5 -4 -3 -2 -2 2 1 I 2 lim I→2 -1 -2- -3- -4 Select all…

A: In this question, we want to select all the correct options by the given graph.

Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 20x − 2 on the interval [3, 7], how many…

A: We have to apply Rolle's theorem.

Q: (a) Find the critical numbers of the function f(x) = x(x - 1)5. X = (smallest value) X = X = (b)…

A: NOTE: Refresh your page if you can't see any equations. . take derivative factor out

Q: Rewrite sin x - 11 6 -7 in terms of sin(x) and cos(x)

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer…

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Q: Using a suitable trigonometric substitution, the integral dx 3 (16x² + 9)² is equal to sin 8+ C₁-<<…

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Q: The limit is equal to 1/3/2 Select one: O True O False lim 818 3n² 2n² + 1

A: We can find the Limits .

Q: sin(2t). Find Əz Ət if z = √r² + s², r = cos(2t) and s =

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Q: lingomi aliluob is to nagogunemi s sed mavenl a. Use the properties of the double integral and…

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Q: 6. Evaluate 1 x² + y² + x² dV, where E = { (®,g, z) |1< n? +g? +z? <4}.

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Q: The series verges Justification: (converges, diverges) by applying the test.

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Q: Graph the circle. (x − 3)² + (y+ 1)² = 16 R -8 46 DE 3 23 -6- -8- 61

A: Standard equation of circle is ÷ x-h2+y-k2=r2 Where,h,k=center of the circle and  r= radius of the…

Q: Solve for this differential equation problem: The part of the normal to a curve, at any point (x,y)…

A: Given The part of the normal to a curve, at any point (x,y) on the curve, between (x,y) and the…

Q: Find the partial fraction decomposition: 7x²+11x+20 x³+4x²+6x+24

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Q: One type of strontium has a radioactive decay rate of 1.4% per day. If 30 pounds of this strontium…

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Q: Is z=xcosϕ ?

A: To determine whether z=x cos φ.

Q: 2. J- dx 25x9

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Q: If sin x = sin(2x) cos(2x) tan (2x) 3 7' x in quadrant I, then find (without finding x)

A: NOTE: Refresh your page if you can't see any equations. . here we have  and the angle is in the…

Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: ! x (x3-2x²+x)(x²+1)* Let f(x) are any constants, which of the following decompositions into partial…

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Q: Find the limit of the trigonometric function. (If an answer does not exist, enter DNE.) lim 8 cos x…

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Q: Calculate dz/du and dz/dv given the following functions: 2x-y x + 3y' = f(x, y) = = Z = x(u, v) =…

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Q: Solve 6 sin X = π X = 2 for the four smallest positive solutions

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Q: Sketch the system. Identify the type of graph within the system. Find the intersection y = x² + 2x +…

A: Given data÷   y=x2+2x+1 and  x-y=-3   y=x2+2x+1 is a parabola and  x-y=-3 is a straight line

Q: n=0 In(n + 4) n+4

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Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1, 1) in the direction of from…

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