Test the series for convergence O a. the series diverges O b. the series converges ∞ 3k k-1!

Q: Find the angle of intersection between the equations f(x) = 3x and g(x) = 4 - x 2 in the first…

A: Given f(x)=3x, g(x)=4-x2.

Q: Find the area of the region bounded by the parabola y² = 2x2 and the line y = x - 5. 16 17 18 19…

A: Given: y2=2x-2 and y=x-5 Now find the point of intersection between the given curves. y2=2x-2 ;…

Q: 2. [e²y - 2y ycos (xy)] dx + [2ce²y - xcos (xy) + 2y] dy = 0

A: We have to find the solution of given differential equation.

Q: The half life of a decaying substance is the amount of time it takes for the substance to reduced to…

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Q: Q2: The equation of the tangent line to the graph of y=r2 and t=4x² at t=1 is (not that x is…

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Q: Question The following table gives the approximate increase in dollars in the average price of a…

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Q: Evaluate the integral i) 2 S² Say e& dady

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Q: Let y = tan(5x + 2). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

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Q: It is estimated that the rate of change of the population of a certain town will be P' (t) = 4+…

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Q: 12 Given that f(x) = 2x 3 + x - 3, evaluate the function f(-2). 11 -69 -21

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Q: -mperature of a northern city from 6 a.m. to 6 p.r 2.3 (in degrees Celsius) and x is the number of…

A: We have to choose the correct option from the given options according to the given information

Q: A pole that is 5625 feet long is leaning against a building. The bottom of the pole is moving away…

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Q: Find the area of the region in the first quadrant bounded by the curve y = √√x² + 5, the x-axis and…

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Q: The graphs of a quadratic function and a cubic function are shown below. Both graphs have integral…

A: Given problem:-

Q: The number of tree species S in a given area A in a forest reserve has been modeled by the power…

A: Given, S(A)= 0.882(A)0.842 Differentiation w.r.t A we have, S'(A)= 0.882(A)0.842

Q: A particle moves along a line with a velocity v(t) = -21 +5, measured in meters per second. Find the…

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Q: 4 + 5x² 4x + x³ dx

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Q: 7. dx ггтV)

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Q: A Ferris wheel has a radius of 12 m and rotates once every 16 seconds. Suppose a passenger boards…

A: We can use cosine equation to solve the question

Q: (a) Write the parametric equations of the line obtained in example 1. (b) Provide the corresponding…

A: Explained below

Q: 5. 6. (log4(x²) dx x (log4 x)² ORA dx

A: We have to evaluate integral

Q: J sec x dx Vin (secx + tan x)

A: As per the instruction, we will be answering the first question. For (4),      ∫secxlnsecx+tanxdxLet…

Q: 29. Verify that the piecewise-defined function 1-x², x<0 x ≥ 0 is a solution of the differential…

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Q: 14 Given the triangle answer to 4 decimal places. X find the length of side x using the Law of…

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Q: / which of the Following series converge and which diverge? Givereasons for your Answer Σ sechn n=1

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Q: Q2: The population of a state is known to grow at a rate proportional to the number of people…

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Q: Determine the volume generated of the area bounded by y=√√x and y=-x rotated around x=5. 2

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Q: Q1: If y=sint and t= sinx, then at x = a) 0 b) c) cosl 2 dx d) -cosl e) others

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Q: EX: Expand fit) = +² o<t<2π in a Fourier Series expansion : Sel: 2L = 2πT 4 44 L=# -41 2tr 4T 2TT 21…

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Q: A company produces a special new type of TV. The company has fixed costs of $480,000, and it costs…

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Q: dr. T About OX -2 2 y=√16-1²

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: he vector, parametric, and scalar equations of the plane for each of g situations: 1961 301 il bari…

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Q: Find the linear use it to estimate ln(1.44). L(x) = In(1.44) approximation of f(x) = In x at x = 1…

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Q: X912 65. f dx is equal to - √1+x" (A) = log(x² + √√x+1)+c 7/2 (C) 2√1+x" +c HT (B) log +C x" 11/2…

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Q: passes through the point P(3,7,2) and is perpendicular to the plane 3x − 5z – 7 = 0. -

A: The given point is P3,7,2 and the given plane is 3x-5z-7=0.We need to find the vector equation of a…

Q: Enclosed by x² + 4y² = 16

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Q: A Prove that 1 B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x²+y²…

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Q: Select all that apply. Solve this equation; domain 0° ≤ ≤ 360°; answer to the nearest whole degree.…

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Q: Q5: If y=tant and x = cost then at t= is (not that these functions in N) dx a) -1 b) 0 c) d) 1 e)…

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Q: Differentiate and simplify this function f (x) = x2/3 sin(x)

A: We have to find the derivative

Q: Evaluate the integral T 22 P" sin cos e de dode Hd 0 H₂

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Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x - 3y - 2…

A: Given: y=√(x-2) , x-3y-2=0

Q: -S² √√x" dx -2- ។ (X) 5 JX dx -2

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Q: Consider the function Step 1 of 3: Find lim f(x). x--6- f(x) = x²2 + 12x + 22 19x + 100 if x < -6 if…

A: Given.

Q: 8- Find the derivative of (x²+1)x

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: Find all solutions to the differential equation. Use c to denote an arbitrary constant. y' = x ln(x)…

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Q: A b. C find an equation of the tangent to the curve at the given point (T/6,1) 4 sin ² x y = + y =…

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Q: 6. show that the complex Fourier series of the function; f.(.t.) = t ..。. st.s.1. is...:. i2nt e j…

A: Fourier series of function is given.

Q: Q/Find the Taylor Polynomials of orders 0,192 and 3 generated by fat F(x) = Sinx 29=0

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