6. f(x) = X a. lim f(x) x-0* b. lim f(x) X-0 c. lim f(x) X-0

Q: √x + 4 In(9-x) Determine where f(x) is continuous, algebraically. (Enter your answer using interval…

A: We have,  f(x) = √(x+4) /ln(9-x)

Q: /2 31. [/² esc 1 cott dr 33. f'(1 + r)' dr 32. [csc²0 de -S²² ²+1 ds 34.

A: We have to Determine the value of integral.

Q: stance in between the point P

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Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r…

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Q: 1 n=3nln n-n K

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Q: ii. Consider the following differential equation: d²x dx dt² +5+8x = f(x) where f(x) is the input…

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Q: 3. Differentiate sin a 1+cos z with respect to x and hence, find S -dx 1+cos a

A: We need to first differentiate then solve integration.

Q: Draw a sketch of the graph of f(x) = 2√x + 1 − 1. Explain the trans- formations of the graph of…

A: Explaination of the answer is as follows

Q: Evaluate the following: To evaluate the limit of the expression lim(x,y) →(0,0) (xy + 1)/(x^2 + y^2…

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Q: 8. (a+b) The angle between vectors a=3 units and units anda is 90°. Calculate 5 to one decimal…

A: The angle between vectors  and  is 90 degrees.

Q: Question 1 Let 0 = cos¯¹(-³) where 0 ≤ ≤. Find the exact value of 0.

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Q: Estimate the slope (slope = rise/run) of the tangent line to the curve. 10 9 8- 7- -6- 5- -1 0 N. -3…

A: (i) To estimate the slope of the tangent line to the curve in the following figure.(ii) To estimate…

Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

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Q: Verify that Rolle's Theorem can be applied to the function ƒ (x) = x³ – 11x² + 38x − 40 on the…

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Q: √2-y² X √x² + y² dx dy

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Q: 2x Find the derivative of Y = e²ª sin¯¹(x) + ln(x) y

A: y=e2xsin-1x + ln(x)Find the derivative of the given function.

Q: Monthly sales of a particular personal computer are expected to decline at the following rate of…

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Q: dy Solve the given differential equation by using an appropriate substitution. The DE is of the form…

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Q: 2. Sketch the line = (-4,-4) + t(6,8).

A: To sketch the line r=(-4,-4)+t(6,8)

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

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Q: The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at…

A: Given, the graph of the function f(x). We have to select all the true statements about the…

Q: Σ (4/5) " n = 5

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Q: First make a substitution and then use Answer: integration by parts to evaluate the integral [2 sit…

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Q: Let f(x) = log6x and O True g(x)= For all x g(x). O False

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Q: Evaluate the following indefinite integral. 36e4x √√3+ ex dx Do not include the constant "+C" or any…

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Q: Evaluate the integral. 66² = Step 1 30 6x² + 7x + 1 +6²= Q(x) = The integrand of 30 where P(x) = 30…

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Q: Find the derivative of the given function. y = (x2 - 4x + 4) e9x/4 기 = dx

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Q: 9. Determine the exact point on the line x + 2y = 2 that is closest to (0, 0).

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Q: We will evaluate the following improper integral: ∞ I 1.₁0. dx (x2+3)2 First we will do the…

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Q: Use the graph below to find the indicated limits. If a limit doesn't exist, state DNE. If value…

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Q: Find the derivative of y = ○ COS X 4 sin x - 4x cos x sin² x 4 sin x + 4x cos x sin² x 2 ○ 4x cos x…

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Q: Find the derivative of y = -10x¹ sin (2x) + e cos 2x

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Q: A space shuttle program involved 135 manned space flights in 30 yr. In addition to supplying and…

A: We have to Determine the angular speed of the shuttle.

Q: The count in a bacteria culture was 900 after 15 minutes and 2000 after 35 minutes. Assuming the…

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Q: When we draw the free-body diagram of a joint, how many independent equation of equilibrium can we…

A: When drawing the free-body diagram of a joint, we can apply equilibrium to determine the forces…

Q: 21. If u and are collinear and the magnitude of u is 7 times the magnitude of v, write an expression…

A: As per the Bartleby guidelines, answering only first question as the other questions are not the sub…

Q: Given the function h(x) = 3x 1 find the inverse function h¹(x). " 2x - 1'

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Q: Suppose the line tangent to the graph of f at x = 4 is y=6x + 1 and suppose y=2x-3 is the line…

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Q: x sin x lim x-0 1- cos x

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Q: Calculus [The following integral can be solved in several ways. What you will do here is not the…

A: By using the trigonometric substitution , to evaluate the following integral.

Q: On the grid below, a) label the axes: x, y, and z b) plot the point P(0,4,0) c) draw the vector OR =…

A: Here we show that in three dimensions given point and vector.

Q: {(1,5), (-2,3)} is a spanning set for R². Express the vector (4, -3) as a linear combination of the…

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Q: 5. A certain computer that is purchased today depreciates in value according to the function (t) = =…

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Q: Let f(x) = 11x³ over the interval 0 ≤ x ≤ 1. Set up the integral for the surface area generated by…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the maximum and minimum values of the function f(x, y) = x²y subject to 5x² + 4y² = 60 =

A: The function isf(x,y) = x2 y5x2+ 4 y2 = 60Let g(x,y) = 5 x2+ 4 y2 -60Differentiate f(x, y) with…

Q: Show that 2y" - y - y = 0 when y=e* + e.

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Q: Find the inverses of the matrices in Exercises 39-42, if they exist. Use the algorithm introduced in…

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Q: Consider the following function. f(x, y, z)=√√x² + y² + z² Find fx(x, y, z), fy(x, y, z), and f₂(x,…

A: We have,    f(x) = √(x2 + y2 + z2 )Point: ( 6 , 2 , 9 )

Q: (2) True or False: a) Local extrema can only occur at critical numbers.__ b) Everywhere there is an…

A: As per bartleby guidelines only one question is allowed to solve with maximum 3 sub parts , so here…

Q: We will evaluate the following improper integral: I [ª da (22+4)2 First we will do the indefinite…

A: We solve this integration problem by using general property of integral.