Test the series for convergence or divergence. 7 In 2 Select the correct answer. O the series is divergent the series is convergent 7 In 3 + 7 In 4 7 In 5 + 7 In 6

Q: First four terms of the sequence are: O O O ○ ○ O 6 {ff, 5 14 9 n²+5 n 1+4 n 61 36 26' 14 { 14/1/2,…

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Q: If f(x) = 4x + 14, find the slope of the secant line between the values of *₁ = 9 and ₂ = 2.

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Q: L4Q5. Find the 15th term of the sequence using the explicit formula: 8 × (3)(n - 1). A.38,263,725…

A: The given term is 8 × (3)(n - 1).

Q: 5. Find the specific solution of the differential equation Oy=ex² O y=-1- ²³/2 O y=-ex None of these…

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Q: Find the volume of the given solid region in the first octant bounded by the plane 12x+12y + 16z =…

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Q: Compute R6, L6, and M3 to estimate the distance traveled over [0, 3] if the velocity at half-second…

A: We need to find R6, L6 and M3

Q: Enter in form a + bi the complex number z which has an absolute value 2 and argument 2/3 π.

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Q: XP xh+qx X 2+ X-2 f

A: This question can be solved using the concept of integration by partial fraction.

Q: my question is:  If one earthquake has a magnitude of 5 on the Richter scale and a second…

A: Topic:- algebra

Q: Let y = (2x + 3 sin(x))4. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

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Q: If a = (4, 0, 4), b = (3, 4,-4), and c = (0, 4, 5), show that a x (b x c) = (a x b) x c. 60i + 96j -…

A: Solution: Step-1                         Given if a = 4, 0, 4 ,b = 3, 4, -4, and c = 0, 4, 5, show…

Q: Find y' and the slope of the tangent line to the graph of (3x - 4y)7 = 2y2-7 at the point (3,2).…

A: The slope of equation is defined in terms of m=dy/dx

Q: L3Q6. If f(x) = 2x – 1 and g(x) = log x, compute (f – g) (x). A.2x – 1 + log x B.2x – 1 – log x

A: Given; f(x) = 2x – 1 and g(x) = log x

Q: Suppose F(z) = g(f(z)) and f(2)= 3. f(2)=-3, g(3) = -1 and g (3)=-4. Find F(2).

A: Recall: Chain Rule  Let F(x)=g(f(x)) , then F'(x)=g'(f(x)) f'(x)

Q: L4Q10.The first term of an arithmetic sequence is 11 and the second term is 16. Find the common…

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Q: Find the angle between the vectors. (First: v = -21 exact u = i- 6j + k, approximate xx x +

A: topic:- vector algebra

Q: (a) Use differentiation to find a power series representation for f(x) f(x) 00 f(x) = n = 0 What is…

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Q: The radius of a spherical balloon is increasing at the rate of 0.6 cm / minute. How fast is the…

A: Topic - Application of derivatives Volume of sphere=43πr3 where r is the radius of sphere

Q: Given the same three points P (1, 4, 6), Q (-2, 5, -1) and R (1, -1, 1). Find the perpendicular…

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Q: Plz

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Q: The tangent plane to the graph of at the point where (x, y) = (2, 2) (write the appropriate function…

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Q: III) Let f, g, and h be the functions defined below: f(x) = 5* To (²²4) 1) Find h¹(r) and obtain the…

A: Given the function, hx=6-x2x-5 we have to find the inverse function of h and range of h

Q: A share valued at $258.65 pays quarterly dividends in perpetuity at a rate of return of 5.50%…

A: Given that      share price =P= $ 258.65                      rate of return   = 5.50%…

Q: (a) Find the volume of the solids generated by revolving the region bounded by the curves y = 4-x²,…

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Q: (a) Find the area of the region bounded by the given curves x+y=0, x = y² + 3y.

A: x+y=0  -----(1)x=-y x=y2+3y ------(2) for points of intersection y2+3y=-yy2+4y=0y(y+4)=0y=0,-4

Q: Two bacteria cultures are being studied in a lab. At the start, bacteria A had a population of 60…

A: Topic:- exponential growth function

Q: Find the cross product a x b. a ++kb-i+2j - 3k 10 Verify that it is orthogonal to both a and b. (a x…

A: Consider the vectors  a=12i+13j+110k,    b=i+2j-3k

Q: An employee has two options for positions in a large corporation. One position pays $14.25 per hour…

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Q: Identify the function represented by this graph. -5 -4 -3 -2 -1 5 4 3 2 -3 ✔ 1 2 3 4 5 x

A: Topic = Functions

Q: Evaluate f x²-x-5 x(x²-x-2) dx

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Q: Determine whether the following series converges or diverges. n² +1 Σ n² +n +8 n=2

A: We have to find the series is Convergent or divergent.  We can apply limit rule to check it.

Q: III) Let f, g, and h be the functions defined below: f(x) = 5* g(z) = logs (3² — 4) x 1) Find h¹(x)…

A: The given function is hx=6-x2x-5

Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: f(x, y) = y^/x, P(1, 3), (a) Find the gradient of f. Vf(x, y) = = (21+ √51) U= (b) Evaluate the…

A: Topic:- application of derivatives

Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: Find f(x) by solving the initial-value problem. f'(x) = 5ex − 8x; f(0) = 9 f(x) =

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Q: Kiara's grandmother is depositing $1,200 at the end of each quarter into a RESP to s for Kiara's…

A: - Periodic Quaterly Deposit at the end of each quarter is $1200 a). Calculating the Accumulated…

Q: Select the graph that best matches the function. = -4 cos(x + ose y = O a) TL (-1/2, 4) (3x/2, 4)

A: Given equation:- y=-4cos(x+π/6)  To find:- Sketch the graph of given equation

Q: What is the integral that represents the length of the curve from x 2 to x = 4. Select one: 4 O…

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Q: Sketch the graph of f ( x ) = 2x³ - 3x² + 3 , indicating the points of inflection and the intervals…

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Q: Convert the point (ρ,θ,ϕ)=(6,11π/6,π/2)to Cartesian coordinates. Give answers either as expressions,…

A: Convert given spherical polar coordinate in to Cartesian coordinate as follwing:-

Q: Use sigma notation to write the sum. 4 [G)²-1])+ N" i=1 X [(4)²-“() X

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Q: Consider the points P(0,0,6) and Q(-42,6,0). a. Find PQ and state your answer in two forms: (a,b,c)…

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Q: After his receiving his first income, Juan dela Cruz invested P20,000 in a bank for his future…

A: Juan Dela Cruz invested P20,000 in a bank for his future family. The annual interest rate in his…

Q: Flight of a Rocket The altitude in feet attained by a model rocket t seconds into flight is given by…

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Q: rticle subject to a force F(x, y) = (-6y, 6x) moves clockwise along the arc of a circle of radius 4…

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Q: Find a linear equation that expresses the relationship between the temperature in degrees Celsius C…

A: The water freezes at 0°C  is (32°F) and boils at 100°C (212°F)

Q: Calculate the derivatives (f(g(x)))' and (g(f(x)))' if f(x) = x² g(x) = 1 8x + 1 (Express numbers in…

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Q: |-2 Evaluate the triple integral ²³ cos (y²) dz dx dy.

A: Here we have to perform triple integration

Q: Using Lagrange multipliers, find the maximum and minimum values of the function f(x, y, z) = 8x - 9z…

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