Express as a single logarithm and, if possible, simplify. log (x²-2x-35) - log (x²-25) log (x²-2x-35) - log (x²-25) = (Simplify your answer.)

Q: Evaluate the following integral. 3 5x(x - 3)dx 0

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Q: 2. Use reduction formula to evaluate the integral: fsins x dx.

A: Reduction formula

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Q: Find r(t) if r'(t) = 4t³ i + 5t+j + √tk and r(1) = i + j. r(t)

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Q: lim (tan x) cos x x-2 X-

A: This question is based on limits of 0infinty indeterminate form.

Q: [ (cosx+2sinx) COSX dx

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Q: State the order of the given ordinary differential equation. (1 x)y" 9xy' + 2y = cos x Determine…

A: state the order of the given differential eqation . and detemine whether the equation is linear

Q: Find f′(x), if f(x)=(x4+1)(3x−1).

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Q: 1-9 13-9 X x-h 2 3 . sin (lnx²) sinx 2-9 It cosx .dx 4-9 cotx.dx хр

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Q: Find the general solution of the given differential equation. x²y' + xy = 8 y(x) = Give the largest…

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Q: Calculus I Consider the following tables

A: We have to solve given Questions.

Q: The exponential function given y H(t) = 80,031.49(1.0483)', where t is the number of years after…

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Q: Consider the following function, f(t) A. All reals. B. All reals except t = 1 and t = -1 C. All…

A: f(t) = t/(1-t)2 domain means input value which we can input in function and function is valid f'(t)…

Q: Find the inverse function of f(x) = = Specify the domain for f−¹(x) ƒ-¹(x) = x² - 9 Domain of f¹(x)…

A: Given that,

Q: IF A [-3 6 -2 3 3 0-3 0 0 12] 06 3-6 -3 0 121 60-6 3 6 6] Option 5 6. Option 4 The Cofactor Matrix…

A: First we will understand  the term and then solve it.

Q: }} If y cos(xy) dydx = x=0 y=0

A: Here we have to find the integral.

Q: let a = (-1 - 1) and b= (t u v w). define a functionn F: a TO B BY FOLLOWINNG ARROW DIAGRAM

A: let a = (-1 - 1) and b= (t u v w). define a functionn F: a TO B BY FOLLOWINNG ARROW DIAGRAM

Q: At what point do the following lines in R³ intersect? l₁ : (x, y, z) = (1,2,1)+ s(1,0,1), l₂ : (x,…

A: See the answer below

Q: Which of the following graphs represents the function g(x) = x(x + 1)²(x − 2)? g(x) 4 4 3 g(x) 4 3 O…

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Q: Find f''(x). f(x) = (x²+6) 6

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Q: Show that the following equation [ has a solution on (0, 2). 42-1 = πX 2 5 cos(-

A: The given equation,       4x-1=5cosπx2

Q: At what points of R² is the following function continuous? 17 f(x, y) = x5 (y² +81)

A: Solve the following

Q: 7) lim (cotx +cscx) XIR

A: lim      cotx + cscx x -->π lim      cosx/sinx + 1/sinx x-->π lim      (1 +cosx)/sinx x-->π…

Q: State the order of the given ordinary differential equation. (sin e)y"" - (cos e)y' = 3 Determine…

A: The order of a differential equation is the order of the highest derivative present in the given…

Q: Follow the steps below for the given function. xy5y - 8 = 0 Solve the equation for y. y = 8 x-5…

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Q: 16 f(x) = x² + x>0 " X (a) Find the relative extreme point (s) of f; (b) Find the point (s) of…

A: As per our guidelines we are supposed to solve only three sub parts of the problem. For the first…

Q: 3. Determine whether the function is continuous at r = 5. 2²-42-5 2-5 x 5 D

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Q: Determine whether the differential equation (4x² - 2xy + 5) dx + (7y² − x² + 4) dy = 0 is exact. If…

A: The given differential equation is;  (4x2-2xy+5)dx+(7y2-x2+4)dy=0.

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 – 3x)y², y(0) = 8…

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Q: 1. Evaluate the improper integral 150 xe dx or state that it diverges.

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Q: Find the general solution of the given differential equation. 2 dy dx - + 6y = 3 y(x) = Give the…

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Q: A function f and a point P are given. Let correspond to the direction of the directional derivative.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: a) Find the symmetric equations of a line through the point po(2,-3,5) and perpendicular to the…

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Q: ) Find f'(x) given that f(x)= 2x² + 3 x² - 5x+2

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Q: Q2) find the absolut maximum values and minimum value of the function f(x, y) = x² - 2xy + 4y on the…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x sin x n = 1 f'(x) n = 2…

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Q: Find the solution of the given initial value problem. ty' + 2y = sint, y = 1, t> 0 Y ||

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Q: Q31 Find the value of Q, where Q = M/N. " 6 3 1 M= 7 -2 4:07 1. Add file 1-3 4 1 91 3 7 TO N=1 3 L2…

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Q: need helping understanding this concept And why each statement is false or QUESTION 1 Check all…

A: We have to consider the given statements are true or false according to the given information

Q: (x+y cot) dy-ydx = 0 (Homogeneous)

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Q: Rewrite the given function with a rational exponent. 7|X 8 = y In X + 8 = In x + 1 || In x + 00 8 00

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Q: y = x42x³

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Q: Use the Chain Rule to differentiate the following function. f(x) = (3x² + (4x-5)4)7 f'(x) =

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Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

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

A: Newton’s Law of Cooling Formula The greater the difference in temperature between the system and…

Q: a. Find the linear approximation for the following function at the given point. b. Use part (a) to…

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Q: Q1) find the critical point of the following equation - g(x, y) = x² + y² + 2xy − 6x - 3y + 4

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Q: Q6) Test the convergence of the following (n+1)(n+2) 1) Σ=1 n!

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Q: First use appropriate properties of logarithms to rewrite f(x), and then find f'(x). f(x) = 2 In…

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Q: Q4:A/ By using Linear equation solve the first order differential equation y' + sec(x) y = cos(x)

A: Given y'+sec(x).y=cos(x)To find solution Of LDE: