Find the length of the curve y=In (cos x), -≤x≤0. The length of the curve is. (Type an exact answer.)

Q: Determine the derivative -d/dv y = 2x³ + 5x - 6 y 1 x² 3x 6x³ + x² − 10x − 3 -

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Q: 1. INTEGRALS AND ITS APPLICATIONS x2- √(¹-2)² dx S

A: Solution is here

Q: lim (lnx) = . x →+∞

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Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

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Q: lim x²e-x x →∞

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Q: cot3x Lim X-o cotx 0

A: Given limx→0cot3xcotxTo evaluate the limit:

Q: The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: Let's find rate of area increasing when W=4cm and l=10cm.

Q: Determine the 3rd derivative of the given function f(x) = (3x² - 5x + 6)4.

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Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

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Q: formula for the sum of the first n terms of a geometric sequence to find the sum of the first 11…

A: Given query is to the sum of the 11 terms

Q: A street light hangs 24 ft above the sidewalk. If a man 6 ft tall walks away from the light at the…

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Q: lim (x-7) tan x x→2 플

A: The objective is to evaluate the limit.

Q: MEAN VALUE THEOREM Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given…

A: Mean value theorem is valid.

Q: L(sin 2t cos 2t) Your answer

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: Given that, Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from…

Q: Evaluate the double integral [[ cos(x + y) dA, where R is the region bounded by the lines y = r and…

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Q: What is the general solution of xy(xy³ −1)dx + x²(1+xy5)dy=0? (A) 2x5y³-3x²= Cx² B 2x³y5-3x2= Cy²…

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Q: Evaluate the iterated integral by converting to polar coordinates. 2x - x² [²√²-2² 9√ x² + y² dy dx…

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Q: Find the volume generated by revolving about the line y-2=0, the area bounded by x^2=8y and the line…

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Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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Q: Find the average value of the function f(x, y) = xy over the triangle with vertices (0, 0), (1,0)…

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Q: it was estimated that constructing a fence for a project could be done by 11 workers in 15 days. at…

A: Let 'n' be the number of workers. Let 'd' be the number of days required Let WT be the work done…

Q: 3. Use Use the disk method to determine the volume of the solid obtained by the revolving the region…

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Q: Evaluate [C sin(x + y)dxdy. Answer: 0

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)= x² + 2x…

A: Using disc method, volume is evaluated.

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

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Q: = 4 R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

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Q: = (x² + y² + z²) −½, then + + 8²v მ2u 8² 8x² მ2 82² If v=

A: v=x2+y2+z2-12 Now,  ∂v∂x=∂x2+y2+z2-12∂x       =∂x2+y2+z2-12∂x2+y2+z2×∂x2+y2+z2∂x…

Q: C) (-∞,1]

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Q: 17. Find the volume of the solid that results when the region enclosed by y = √x, y = 0, and 2 = 9…

A: According to our guidelines, we can answer only the first problem or first three subparts of a…

Q: Numerical Integration: r2 1 S² = = X 0 1. dx

A: Please find the solution:-

Q: Question 1 A body cools from 72°C to 60°C in 10 minutes. How much time (in minutes) will it take…

A: We will use Newton's law of cooling to solve this question.

Q: y" - 3y' + 2y = 6

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Q: Əz 5. Givenz = y -4x ?х 6. Find of z = In(xy) a²z 7.Find of z= x³ + 5x²y + 6 əxəy Find дz

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Q: lim (e²x + 2) 8118

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Q: Which of the following CANNOT be solved by method of undetermined coefficients? 1 A (D²+1)y=. cos x…

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Q: Iff and g are continuous on [a,b] and f(x) ≥ g(x) for all x € [a,b] th then A True B False [ f(x)dxz…

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Q: Given than f(x) dx = 4 and A None of the given choices ℗ 25 (2) dx = [1 (2) de B f(x) © f (x) dx =…

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Q: 6. Determine the area of the region bounded by x = −y²+ 10 and x = (y 2)²

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Q: 1. f In(x+2) dx 2x+4 2. fx² ex dx 3. f tan³x dx 12

A: We know that integration of xn is xn+1 /n+1. And integration of 1/x is lnx +c.   Here i attached the…

Q: 1. Find the area of the region that lies inside the cardioid r = 1+ sin and outside the circle r =…

A: We need to find area.

Q: S dx secx + 1 Transforming Ⓒ / + A -dz 1+z² 2-2z² (B) 1+z² C 12²+2 dz Ⓒ √ 1+2²2 dz D 1-z² -dz using…

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Q: Given [ f(x) dx = 0 and 11 0 11 6 55 6 rwax = 11 6 " evaluate S злах-п -1 2f(x)dx

A: Given,∫-11f(x)dx=0,∫01f(x)dx=116,To find ∫013f(x)dx-∫-102f(x)dx

Q: y = Arctan ( 2+x 1-2x

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Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

A: Let's find time taken 1/2 the original amount of radium to decompose.

Q: 2. lim x sin(1/x) X18 ex+2x 3. lim X18 ex

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Q: 2 d So (x + 2)²0 Using Trapezoidal method spaces) dx for n=4 is equal to Blank 1 (use 2 decimal…

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Q: The length of a rectangle is given by 4t - 3 and its height is √2t, where t is time in seconds and…

A: The area of a rectangle with length L and height H is given by A=L×H. We use chain rule , power rule…

Q: SHOW COMPLETE SOLUTION (NO SHORTCUTS PLEASE) (Differential Equations) Particular solution of y" -…

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Q: Q3/ Solve the following. Choose two only. 1. lim x lnx³ X-0 2. lim x sin(1/x) 818 ex+2x 3. lim 818…

A: According to the question, we will calculate the limits of any two subparts.