Let a = 3/2 + 34. (a) Compute a³ and write it in the form pa + q where p and q are integers. Use this to show that a is an algebraic number. (b) Prove that a is irrational.

Q: Consider the following limit. 2-x x + 2 2 lim X→2 Simplify the rational expression as much as…

A: let  I=limx→22-xx+2-2we know  a2-b2=(a-b)(a+b)

Q: Determine the right and left behavior of the following graphs. Write "R" if it rises and "F" if it…

A: Follow the procedure given below.

Q: Evaluate the line integral (5,0) to (0, 10). F. dr, where F(x, y) F. dr, where F(x, y) = -yi+aj and…

A:

Q: Q4). Using appropriate substitution integrate [ πx√1 + x² dx.

A:

Q: Evaluate the limit. lim x-0 sin 3x tan 10x

A:

Q: Evaluate the integral (2x + 5) (x² + 5x+8) ² dx 2 by making the substitution u = x² + 5x +8. + C…

A: NOTE: Refresh your page if you can't see any equations. . .................(1) substitute…

Q: dy Which of the following is the slope field of the differential equation = 2x+y²? Give a short da…

A:

Q: Find the domain and range. Draw the graph describe something about the graph. 1. f (x, y) Y V X

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Let u = (-7,4,-5) and = (3,4,-5). Compute the following: uxv= vx u= ūXu= 5 ( x ) = u x (5v): (u + v)…

A: u=-74-5 and v=34-5

Q: Find the sum of the series: n=0 X 5n-3 n!

A: The given series ∑n=0∞x5n-3n!. We have to find the sum of the series.

Q: 1. Use the definition of derivative (not the rules of differentiation) to calculate d (x² + X) dx…

A:

Q: Determine the right and left behavior of the following graphs. Write "R" if it rises and "F" if it…

A:

Q: Hello, I have 3 homework problems I need help with.  lim.       (3/t - 3/ t2+t) x->0

A: Given limt→0(3t-3t2+t)

Q: ||r' (t) x r"(t)|| ||r' (t)||³ r(t) = eti+ e tj Use the formula (t) k(t) = 5 e²+25 (25 elot + e-2t)…

A:

Q: 2 Evaluate lim et² cos(1/x) 2 O

A:

Q: What is the average rate of change (slope) on the interval [1, 2] for the function f(x) = 2x³ - 6x…

A:

Q: Find all the values of x (x - 10)" 10 n=1 The series is convergen from x = > le

A:

Q: h 80 a pdp 3 p=0 (p² +h²) ž

A: Given ρsh2∈0∫ρ=0aρdρ( ρ2 + h2 )32

Q: Find the limit. (If an answer does not exist, enter DNE.) X-2 lim x 2 x² - 4 STEP 1: Factor the…

A: To find the limit

Q: A cubic polynomial with positive leading coefficient is shown in the figure below. y -10 -5 10- 5 -5…

A:

Q: ∞ (c) The curve given by the polar equation r = (a) Suppose a > 0 and be > 0 for all k. Ifak and by…

A: see below the answer and explanation

Q: с 71° 73⁰ b a=13.1

A:

Q: (a) If lim X-3 (b) If lim X-3 f(x)-5 X-3 f(x)-5 X-3 2, find lim f(x). X-3 = 4, find lim f(x). X-3

A:

Q: Given the higher order non-homogeneous differential equation y" — 5y' + 4y = 8ex Solve using…

A:

Q: Does the series k4 k10+ 3 converges absolutely converges conditionally diverges Does the series (-1)…

A:

Q: A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The…

A: given  point P is  (15,V(15))Q is  (25,V(25))slope=change in y values  change in x values

Q: The monthly profit from the sale of a product is given by P = 28x - - 0.2x² - 100 dollars. (a) What…

A:

Q: With your pencil, make a dot on the position of your best visual estimate of the centroid of the…

A: Given,            The triangular area diagram is shown below :

Q: Determine the x-coordinate of the centroid of the shaded area by integration. 29 y 1 26 Answer: x =…

A:

Q: A chemical was introduced into a large swimming pool to determine if it would affect the amount of…

A: NOTE: Refresh your page if you can't see any equations. . the initial amount of algae is 70 kg so…

Q: Fill in the missing numbers of the sequence generated by Euclid's algorithm on inputs 70 and 15.…

A:

Q: The expression 256g³y³√256g³y³ = kg"y where: r = 8 = and k =

A:

Q: Calculate an integral of an irrational function.

A: An integral of an irrational function. ∫dxxx2+x+1

Q: M 7 The flight of Jae and Miguel's rocket t seconds after launch is modeled by h(t) = -512 + 40t + 1…

A: As per our guidelines we can answer only 3 subparts of the given question so kindly repost the…

Q: d dr -x² + e³¹ - tan(x) dy²-sin(y) dy cos(y) +2 d dx -√x+e²

A:

Q: You are given the following functions. (I) y = x²-5 x² +5 (II) y = x² +5 ²-5 (III) y = 5 x² +5

A:

Q: Use the given graph off to state the value of each quantity, if it exists. (If an answer does not…

A: NOTE: Refresh your page if you can't see any equations. .

Q: ute the prime factor Icm(466560, 54000 466560 27 36.5 540000 = 25 33.54 Fy: 2^3* 3

A: topic:- application of algebra

Q: Σ 10(-1.6) is an k=0 Σ 10(-1.6)* k=0 is an alternating geometric series, w –

A: given series is ∑k=0∞10(-1.6)k then we have to check it is converges or divergent since we have…

Q: The graphs of the demand function and supply function for a certain product, are given below. Use…

A: see below the answer and explanation

Q: 4. The partial fraction decomposition of 12 x-1 x+2) n be written in the form of A b + x-1 x+2

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: For the equation y=-sin 2(x-2)-1 -1 determine the amplitude: a) 1 b) 2 c)-2 d) -1 c) 0

A: NOTE: Refresh your page if you can't see any equations. . y=-sin2x-π2-1 here coefficient of the sine…

Q: Find the area of the largest rectangle having two vertices on the x-axis and two vertices on or…

A: We have given to find area of the largest rectangle  Area of the rectangle is given as  A=2xy Put y…

Q: 50. Using different intervals. a. Use an average rate of change over the interval [4, 25] to…

A:

Q: pls. help me in no. 7 letter c and d thank you

A: Please see the below picture for detailed solution.

Q: Consider the solid bounded by the planes x = 0, y = 0, and x + y = 2 along with z = 4x². (a) Write…

A: Given that x= 0 and y=0 and x+y = 2 along with z= 4-x2 we find the volume of this solid generated by…

Q: vector field O The vector field is not conservative (6xy + 8y-3, 3x² + 8x). The vector field is…

A: Please see the below picture for detailed solution.

Q: 4. The graphs of f and g are given. a. State the values of ƒ(−4) and g(3). b. For what values of x…

A: The graph of the functions fx and gx are given, we have to find the given values.

Q: Find the area of the region enclosed by y = 4.25x and x = 4.5 - y². 2+ 2 a Use horizontal strips to…

A: Find the area enclosed by   y= 4.25x and x= 4.25-y2  use horizontal stripes to find the area that is…

Q: Which one of the following correctly finds the Taylor Series and the Interval of Convergence about…

A: