To rationalize the denominator of 45 what value should the numerator and denominator be multiplied by?

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Q: Use local linear approximation to estimate In(1.08)

A: Given problem:- Use local linear approximation to estimate ln(1.08)

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Q: Suppose that f is a function given as f(x) = - x² +x – 2. Simplify the expression f(r + h). f(x + h)…

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Q: 10. Given the supply and demand functions: P = 10+2Q, P = 30 – Q Which of these statements are…

A: Here the given demand function is             P = 30 — Q Supply function is             P = 10 + Q…

Q: Identify the function, whose derivative is defined below: dy (х + h)2 — х2 lim h→0 dx h А. f(x) — Һ.…

A: Given dydx=limh→0(x+h)2-x2hWe know that the limit derivative formula is f'(x)=limh→0f(x+h)-f(x)h

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Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A: integration

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Q: 1. A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on…

A: Question is solved step by step.

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Q: Suppose that f(x) = -9x/6. Evaluate each of the following: f'(2) = f'(5) =

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dy

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Q: Q1. Which of these expressions is NOT factorised? А. X(х + 1)(х + 2) В. (х+ 1)(х+2) С. x (х + у) —…

A: Solving the problem by finding the correct answer.

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Q: . Find f 6x5-25x*+8x3 +43x2-8x-12 (3x-11x3+9x2-11x+6)(9x2+12x+16) dx if this can be reduced to…

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Q: 1. A bumblebee was released and started to travel along a straight horizontal line. The directed…

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Q: 6. For each integral, state which trigonometric substitution you would use to integrate by…

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Q: (a) Put a pair of brackets on the left hand side to make these statements correct. 17-2 + 8-4- 11 -…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Find the coefficient of w2r?y'z? in (2w-z+3y- 2z+2)°.

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Q: Write the integral in terms of u and du. Then evaluate. u = 812 + 1 (Use symbolic notation and…

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Q: Find the arc length L of the graph of r(t). r(1) = t³ i+ t j+V6r? k, 2 <t< 5 k, 2 <t < 5 L = i

A: Given : r(t) = t3 i + t j + √6 t2/2 k 2 ≤ t ≤ 5 Now, r'(t) = 3t2 i + j + √6 t k Arc Length :

Q: 4x +2 (x + 1) >7+x

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Q: At the beginning of an experiment, a scientist has 176 grams of radioactive goo. After 210 minutes…

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Q: Determine whether the vector field F(x, y, z) = x'5 i + y'5 j + z!5 k is free of sources and sinks.…

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Q: 10. Find the position function s(t) given acceleration a(t)= 2t if v(2) = 0 and s(2)=1.

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Q: Find T(t) and N(t) at the given point. r(t) = 10 cos(t)i + 10 sin(t)j + tk; t = 2 TE) -| 6) =

A: we have to find unit tangent vector and normal vector.

Q: Write the equation of a sine or cosine function to describe the graph.

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Q: 9. 5- 8. 7- 4- h(x) 6- 3- 4 g(x) 3. 17 4 3. X-values 1 3. X-values 4 g(x) If f(x) then h(x) f'(1) =…

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: If an arrow is shot straight upward on the moon with a velocity of 57 m/s, its height (in meters)…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where U + dy

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Q: Evaluate the definite integral. Sols i + e*j+ t k at O e6 - 1 i+ 6 1 k i- i- (e 6 1 6 2

A: We know that integration of xn is xn+1/n+1. That is power rule of integration.     Here i attached…