23. Express each of the following as a logarithm. Use a calculator to evaluate your answer correct to one decimal place. a) 6* = 27 x+2 b) 4**² = 23

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y² + z² (8,…

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Q: For the function, do the following. f(x) = 1/x from a = 1 to b = 4. (a) Approximate the…

A: The function fx=1x from a=1 to b=4

Q: When Newton's Method is used to approximate the root of f(x) = x³ + 2x² - 1 in in the interval [0,…

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Q: (a) Determine whether the series n=1 n+1 n³ +3 is convergent or divergent.

A: Solution: ∑n=1∞n+1n3+3

Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: The length of a rectangle is three times its width. If the area of the rectangle is 108 yd², find…

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Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these…

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Q: at ch Use the Fundamental Theorem to show that the following is true. a f b C b [ f(x) dx = ff(x)dx…

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Q: A math teacher won a lottery that pays $1,000 per month for the next 20 years. But, he prefers to…

A: To find out the amount that the teacher will accept now.

Q: 72. Function f(x) = cos 2x, π 0<< 2 Real Number a = 1

A: Given: fx=cos2x 0≤x≤π2

Q: 11. (2.3.34) Let f: B → C and g: A → B be functions. (a) Prove or disprove the following statement:…

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Q: 16. x²y" (x) + 5xy' (x) + 4y(x) = 0 ; y (1) = 3, y' (1) = 7 17. x³y"(x) + 6x²y"(x) +29xy' (x) -…

A: The given differential equation is;  x2y''(x) +5xy'(x) +4y(x)=0, y(1)=3, y'(1)=7.

Q: 3. [x²cos2x dx

A: The given integral, ∫x2cos2x dx Note:    Multiple questions are given, we are answer only one…

Q: Find all values of x and y such that Px(x,y) = 0 and Py(x,y) = 0 simultaneously. P(x,y) = 5x²2 -…

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Q: e) Find the linear approximation of the function f(x, y, z) = x³y² + z² at the point (2, 3, 4) and…

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Q: 2) Evaluate |x + 11 dx

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Q: integral

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Q: Find the limit of s(n) as n → ∞0. ( s(n) = 4 n n(n + 1)(2n + 1) 8

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Q: Cut out squares (of the same size) from the four corners of a square cardboard of given side length…

A: The side of the square = L  let the length of the square = x,

Q: 2. (x + y) dx + (3x + 3y − 4) dy = 0

A: The given differential equation is;  (x+y)dx+(3x+3y-4)dy=0.

Q: Solve the given differential equation by undetermined coefficients. y" + 7y' + 6y = 18 y(x) = || X…

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Q: Prove that the graph of the function y = x² −3+1/x has at least two x-intercepts in (0,2).

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Q: Select the correct answer. y = 6x4 - 8x² + 5x 4 y = 5x² - 6x² + 8x + 3 y = 6x²³ - 8x² +5 Oy=x²-8x²³…

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Q: 3 Solve the following ODES by Inverse Operator method 2 • (B³² +1) y = cos x 11

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Q: -4 -2 (a) x=¹t+3, y = 2² VX (b)x=²2t, y = √t 11 (c) x = ²³ - 2t, y = 2² - t ✓X III (d) x = cos(5t),…

A: Please see the below picture for detailed solution.

Q: Using Desmos or other graphing software, sketch the graph of y = sin (2x). a. Using the tangents,…

A: Y=sin(2x)

Q: Verify the identity. sin(x) + cos(x) = sin(x) cos(x) sec(x) + csc(x) sin(x) + cos(x) sec(x) + csc(x)…

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Q: 14) At what point on the graph of f(x) = instantaneous rate of change? a. x8, x = 2 b. x = 4…

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Q: Evaluate the function for the given value of x. r(x)=3x, p(x)=x2+6x,(p-r)(x)

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: Find the derivative of y with respect to x. 1 y=x' In (x)---x obra d we do O A. 7x5-x² OB. 8x5-x2…

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Q: h tin tly Suppose that the graph below is the graph of f'(x), the derivative of a function f(x).…

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Q: Constraint 1. V= 32000 cm³ xyz = 32000 g(x, y, z)=xyz-32000 vg = (y², xz, xy) function SA= xy + 2yz…

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Q: Use the substitution t = -x to solve the given initial-value problem on the interval (-∞o, 0) x²y" -…

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Q: ƒx(2x−1) dx 2 √x³√x²+4 dx

A: for (1),     ∫ x2x-17dx=∫ 128x8-448x7+672x6-560x5+280x4-84x3+14x2-xdx=∫ 128x8dx-∫ 448x7dx+∫…

Q: 3 Find the Cartesian coordinates of the following points (given in polar coordinates): 3.a (√2, π/4)…

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Q: A white wine at room temperature 70° F is chilled in ice (32°F). If it takes 15 minutes for the wine…

A: Given that , Room Temperature T0=32°F

Q: down oes... not a precise m However, with ann an algebra c concave do rate of chang creasing y…

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Q: Given that log a ( 2 ) = m and log a ( 3 ) = n , write exact expressions in terms of m and/or n for…

A: Write expression in terms of m and n for each of the following.

Q: Find the directional derivative of the function at P in the direction of v. 1 = √₂ (i+j) f(x, y) =…

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Q: For the function f(x,y,z) = x rr fy 11 he e = 11 f₂ = N fyz 10 8z+1 -9 8z+1 (9y-10x)8 (8z+1)² 11 72…

A: The given function is;  f(x,y,z)=(10x-9y) /(8z+1).

Q: 8. A rocket is fired into the air with an initial velocity of 98 m/s. The height (h) of the rocket…

A: The height of the rocket after t seconds is given by the expression h=98t-4.9t2

Q: 1. (Use a calculator) Write down the equation used to evaluate the following expressions, and then…

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Q: Use long division to find the slant asymptote f(x)=2x2+7/x

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: Use the power series f(x) = In (1-x) = -for-1sx<1, to find the power series representation for the…

A: The power series fx=ln1-x=-∑k=1∞xkk, for -1≤x&lt;1 we have to find the power series for px=9x8ln1-x

Q: f(x)=ax^3+bx find the derivative

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Q: Evaluate the function at the given values of the Independent variable. Simplify the results. g(x) =…

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Q: (a) Determine whether the series (b) Determine whether the series ∞ n=1 ∞ n=1 n+1 n³ +3 is…

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Q: If cos x = 5/11 and the terminal point of x is in Quadrant IV, what is sin x

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