Find the local linear approximation of the function f(x)= square root of (1+x) at x0=15, and use it to approximate the square root of 15.6 and square root of 16.1.

Q: Find the surface area of revolution about the x-axis of y = 4 sin(7x) over the ㅠ interval 0≤x≤ 7

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Q: Use integration by parts to evaluate the following integral. 1 12 S 0 x In 12x dx

A: To evaluate the given integral

Q: 46. If y=xcos(x) then : d²y dx² -= ? -2sin(x) - x cos(x) - sin(x) -2sin(x) + x cos(x) sin(x) إذا…

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Q: A farmer finds that if she plants 95 trees per acre, each tree will yield 35 bushels of fruit. She…

A: We need to find out the number of trees that should be plant per acre to maximize the harvest.

Q: Use spherical coordinates. •JJJ* Evaluate te+² y² + z² dv, where E is the portion of the unit ball…

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Q: Which one of the differential equations is exact? Select one: O None of the others. ○ (4xy² + 2xy)…

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Q: 1) Consider an investment of $3000 at 2% compounded monthly. Find the amount in the account after 4…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Suppose C(*) represents the amount of dollars spent every miles travelled. What unit does C'(12)…

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Q: Convert (-1,-31/2) to polar coordinates.

A: Given query is to convert the point into polar coordinates.

Q: Calculate lim x→0 cos x − 1 + x²

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Q: 21. 2(3*+1)=3(2x-1)

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Q: A piece of land is triangular in shape. Two of its sides are measured as 80 ft and 100 ft, and the…

A: Let a and b be the length of the sides and θ be the included anglebetween them.a=80 ftb=100 ftθ=π3…

Q: For the function f(x) given below, evaluate lim f(x) and lim f(x). x-x X118 Provide your answer…

A: Given query is to find indicated limits.

Q: Find the limit or indicate that it does not exist. 3 HET [ ( = = 1 ₁ + (000 + ) ₁ + [Tam ² ₁] ] lim…

A: put limit value as  t=π

Q: Determine all the critical numbers of f(x) = A) X=0 B) x = 1 (c) There is none (D) x=-1 3x x²-1 .…

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Q: g(x) = 200 + 8x3 + x4 a) Find the intervals of increase or decrease b) Find the local maximim and…

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region = = x², y =…

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Q: The intensity levels I of two earthquakes measured on a seismograph can be compared by the formula…

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Q: The polynomial of degree 4, P(x), has a root of multiplicity 2 at x = 2 and roots of multiplicity 1…

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Q: → Limit Review! Evaluate the following limits: lim lim ln x = In x = x →0* a) d) x →∞ lim x → 2+…

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Q: 08/298 1 4:2

A: Topic:-  Binary number system

Q: For the function f(x) given below, evaluate lim ƒ(x) X18 and lim f(x). X118 f(x) = If the function…

A: Given query is to find indicated limits.

Q: 3. y = X x² 9 Curve Sketching Information Domain Intercepts Local maxima Local minima Point(s) of…

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Q: Use the first derivative test to find the location of all local extrema in the interval (0, 2) for…

A: given f(x) = 2sin3x - 5 for maxima or minima step 1) find points where f'(x) = 0step 2) if f''(x)…

Q: Evaluate the limit lim x →∞ 2x³8x² - 6x 22x5x³

A: To evaluate the given limit of the function

Q: 72148 26110 = ?2

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Q: Use the Shell Method to calculate the volume obtained by rotating the region under the graph of…

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Q: Make a sign diagram for the derivative of the rational function. 12x - 60 4x + 20 f(x) =

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Q: The region bounded by f(x) = 0, and y = 0 is rotated about the y-axis. Find the volume of the solid…

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Q: Question 2 A proton moves in a horizontal line. Its position, t seconds after the particle begins…

A: Use the expression for the velocity: vt=dstdt Use the expression for the acceleration. at=dvtdt And…

Q: for each In Problems 21-30, find an explicit formula a, = sequence, determine whether the sequence…

A: The given sequence -1, 23, -35, 47, -59,..... We have to find the explicit formula for the sequence…

Q: What is the geometric ratio of the sides of a Kepler's Triangle?

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Q: A radioactive substance decays according to the following function, where yo is the initial amount…

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Q: Find all values of x for which the tangent line of f(x) = A B С D -9 0,-9 -9,9 0,9 x²+18x+96 is…

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Q: Which of the following is the derivative dy dx dx cot:+1 coty + 1 The answer cannot be found among…

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Q: (P) xp- (e) fx dx (1) √(2x² - 6² xp(x9

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Q: If a, b, c are the sides of a triangle and is the included angle between aand b, find and by…

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Q: Let f(x) = x3 - 8x + 13. Then the equation of the tangent line to the graph of f(x) at the point…

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Q: 2) Consider the DE: (2xy − 6x²)dx + (x² +9)dy = 0 - A) Determine whether the DE is exact or not,…

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Q: lim In(x) In XX x+1 + 1 X --

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Q: For the function f(x) given below, evaluate lim ƒ(x) and_lim_ƒ(x). X→∞ X-18 Provide your answer…

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Q: Differentiate the following functions using INCREMENT method of differentiation: 7. y=9a²x+8b; where…

A: 7 y=9a2x+8b8 fx=3x-810x+79 n=5am+225a2m2-10am+4

Q: Find the centroid of the region bounded by the given curves. y = x¹, x=y4 (x, y) =

A: As we know the expression for the centroid. x=1A∬xdydx and  y=1A∬ydydxWhere: Area=A=∬dydx The given…

Q: 28. On the Richter scale, the magnitude M of an earthquake depends on the amount of energy E…

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Q: . i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence…

A: Limit point of a sequence is that point whose neighborhood is surrounded by infinitely many points…

Q: 2. Find the interval of convergence of the series k²(x+3)k+1 5k k=1

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Q: Find the ratio of an infinite geometric series if the sum is 2 and the first term is 1/2. I

A: As we know the expression for the sum of an infinite geometric series is: S∞=a1-r ; where…

Q: Given z = f(x, y), x= x(u, v), y = y(u, v), with x(−1, 1) = 1 and y(−1, 1) = 2, calculate z(-1, 1)…

A: see below the answer and calculation

Q: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at = 1 and…

A: The polynomial of degree 5, Px, has leading coefficient 1, has roots of multiplicity 2 at x=1 and…

Q: Find the area of the region bounded by the graphs of y = x² x and y = 2x from x = -2 to x = 4.

A: Given y = x2 - x y = 2x from x = -2 to 4 Area of region bounded = ∫x1x2( y2 - y1 )dx