Evaluate the limit: lim_ (x - ln x)* x→0+

Q: Find fx (x,y) and f, (x,y). Then find fx (2, -1) and fy(-4,3). f(x,y)= ex+y+5 fx(x,y)=

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Q: Determine the following integrals: 1.1.1 ļ (cos2x+sin x) dx x+1 .1.2 1₁ JF dx x + 2x+1 2 1.1.3 | ₁…

A: ∫ sin(ax) dx =-cos(ax)a+C       and     ∫cos(ax) dx =sin(ax)a+C ∫xn dx = xn+1n+1+C Note : As per our…

Q: ab c Pq r U V W a. det (2B¹) where B = 4u 2a 4v 2b -q 4w 2c <-r 2p -a+u 3u b. det (20¹) where C =…

A: Given problem:-

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Q: equences . Given that a₂ = 6 and as 96 are terms of a geometric sequence, find a. 2. Given that a10…

A: solution

Q: II. Find the value(s) of x (or the interval of convergence) 2. Σn=0 for each of the following power…

A: The power series is  ∑n=0∞ (-1)n+1(x-5)nn·5n

Q: Evaluate ¹ dx √√9-4x2 a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

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Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

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Q: A payment of $6,500 was made into an account at the end of every 3 months for 12 years. a. If the…

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Q: Q1-A/Find the domain of the following functions. 1-f(x) = √(sin(x) - 1) 2-f(x)=-/In(5x-x²/4)

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Q: 5x4y + y² 2x5 + 3xy' - dy dx O x¹y² + xy³ = 48 O x³y² + y³ = 120 о x²y² - y³ 3 = 56 O x³y² - xy³ =…

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Q: Evaluate the limit: lim (x - ln x)* x→0+

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Q: 4.) Give the general solution of the following ODE: x" + 3x - 4x = 0.

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Q: 2. lim (tanx) (sin r-1) x→

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Q: What is the integral of (2 sec^2x - sinx) dx? * O 2 cosx+tanx + C 2 tanx + sinx + C 2 tanx + cosx+C…

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Q: NUMBER 3 CLEAR AND SIMPLE

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Q: 4 fcos 3x sin³ 3x dx

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Q: Perform the integration. π ¹3 sec³ x tan x dx √2 + secx 0

A: A detailed solution is given below.

Q: 9. A child is flying a kite with a 45-ft string at an angle of elevation of 50°. Which of the…

A: Let's find altitude of the kite in feet.

Q: Stan 3x sec 3x dx 3.

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Q: Is that pi (π)? Or something?

A: Given ,  Area of the region bounded by  y = cosx , x = -π/2 and x = π/2 and the x - axis  We have to…

Q: What is the y = x^3 and y = x^2? O2/5 3/5 6/35 12/35 y-coordinate of the centroid of the plane…

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Q: Evaluate (2x + 3e* - 4) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE A О в Oc O D DE

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Q: The tenth term of an arithmetic sequence is 23, and the second term is. Find the first term. X

A: Let's find first term of arithmetic sequence.  Tenth term = 73/2 Second term = 9/2

Q: Evaluate the integral of 3dx/(2x^2 + 4) from 0 to 0.2 *

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Q: A group of management students are creating a business plan for their proposed shoe brand…

A: We have to find the marginal profit when 100 pairs are sold, production level so the average cost…

Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2, y = 1, and…

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Q: [x xf (x²) dx Which integral is equivalent to the one shown: Oa) f f(u) du √uf (u) O b) S 2 O c) […

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Q: 2 cos xsinx V2+cosx 1. S- -dx

A: Given

Q: PLEASE SHOW COMPLETE SOLUTION.   Find the area bounded by y = 1/4 x^4 − x^2 and y = x(x − 2)(x +…

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Q: Why is it =10πr33? particularly, why is the value 33?

A: Let's solve.

Q: 3. A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^3, y- axis,…

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Q: The area bounded by the graphs of y = 2 - x^2 and y = x^2 revolves about the x-axis. Determine the…

A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…

Q: Using Laplace transforms, solve the initial value problem y" − 2y' + 10y = 0, y(0) = -3, y'(0) = 3.…

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Q: So x² (a²-x²) ³¹/2² dx

A: A detailed solution is given below.

Q: Evaluate the following integrals. Show the solution.

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Q: Perform the integration. (sinh x)(coth→ x + csch3x) dx

A: A detailed solution is given below.

Q: Evaluate the following limits 1. lim (2x+x) x → +00 e2x +In x

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Q: = t² - 6t + 8, The velocity function of a particle moving along a horizontal line is given by v(t)…

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Q: The pedals of a bicycle are mounted on a bracket with centre 27.5 cm above ground. Each pedal is…

A: 1) Center = 27.5 cm  Radius = 17.5 cm  Rate = 10 cycles per minute =&gt; Rate (ω) = 1/6…

Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…

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Q: Evaluate the integral cosx dx from í/3 to π/2 * 0.134 0.500 0.293 0.707

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Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: dx ढळ 2])

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Q: (x² - 12x + 9) dx (x²-3x + 2)² 2. √(x²

A: Given: I=∫x2-12x+9x2-3x+22dx   As we know that; The Power Rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: Determine whether the series 1/4 O 1/2 3/4 + Ex=1 ( 2² - 2 +²+1) 2k+1 0 1 converges and if so, find…

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Q: c4 So So (6x² +9y²) dx dy

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