Let lim f(x) = 3 and lim g(x) = 15. Use the limit rules to find the following limit. x-6 lim f(x) x-6 9(x) x-6 lim x-6 f(x) g(x) (Type an integer or a simplified fraction.)

Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y, x = s + 2t-u, y = stu²…

A: Given: To Find: To find

Q: Find f'(x) using the QUOTIENT RULE if f'(x) = Find f'(3). f'(3) = = f(x) 6-x² 6+ x2

A: The answers are as follows: f′(x)=(6+x2)2−24x​. f′(3)=−258​.Explanation:Steps and explanations are…

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A: The tangent line to the graph of  is shown below.(a) To find the coordinates of the the points P and…

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Q: Let аз +-(633) A and suppose that det A = 8. Determine det B if b3 B = a15c1a2+5c2 a3 +5c3 -3c1 -3c2…

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Q: Find the curvature of the curve (t) = = (4t, 4t2,35) at the point t = - 2. Give your answer to 2…

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Q: Find the volume between the surfaces using double integrals in polar coordinates: z = x2+y2+3, z = 0…

A: Summary:The volume between the surfaces is 7π​/2 cubic unitsExplanation:Here's the step by step…

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A: The objective of this question is to find the absolute maximum and minimum values of the function…

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Q: Suppose a person wants to travel D miles at a constant speed of (60+x) mi/hr, where x could be…

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A: To minimize the amount of paper used for a page with a fixed print area, we need to find the…

Q: (If an answer does not exist, enter DNE.) (2,30) 20- 20 |(2,5) (9,9)

A: graph of f(x) is given

Q: 11. A snowball melts so that its radius decreases by 0.2 cm/min. Find the rate at which the surface…

A: A snowball melts so that its radius decreases by 0.2 cm/min. To find the rate at which the surface…

Q: 3. Verify sin(x) + cos(x) cot(x) = csc(x)

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Q: Polar formulas 4. Assume r = f(), with on [a, ẞ]. Write the following formulas. AREA ARC LENGTH

A: Step 1: Step 2: Step 3: Step 4:

Q: VII) Solve the rational inequality. Express your answer using interval notation. 4x 1. x²-4 I- -3 2.…

A: 1.xϵ⟨−2,0]∪⟨2,∞⟩ 2.xϵ⟨−2,3] 3.xϵ⟨2,4⟩   Explanation:

Q: Please see atrached. Thank you, and please circle your answer.

A: The objective of this question is to find the derivative of the function x^n, where n is a constant.

Q: Let y(x)=3 Estimate the slope of the tangent line of y(x) at the point x = 2: nonzero numbers after…

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Q: Given y= 0.3 Sin (0.2 - 0.1 x) determine • four roots • three maxima and minima • range , period…

A: To solve this, let's first understand the given function y = 0.3sin(0.2 − 0.1x): Roots:  Roots of…

Q: At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship…

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Q: HELP ASAP

A: The answer is given below.Explanation:

Q: Given the function f(x) = 10 log(x + 3), find the area of the region bounded by the graph of y =…

A: Given: To Find: To find the area of the region bounded by the graph of , the x-axis, and the line .

Q: Use the quotient rule to find the derivative of the given function. 2 8t² -5t f(t)= 9t +2 f'(t) = ☐

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Q: HELP ASAP

A: Answer: We calculated that    ∫04​∫16−y2​64−y2​​7+x2+y21​dxdy+∫48​∫064−y2​​7+x2+y21​dxdy…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. (7+2) y = √1+ex,…

A: Step 1:​Given a function here:y=1+ex​,To find: The exact area of the surface obtained by rotating…

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Q: Ay 15 12 9 Solve graphically by the intersection method. Give the solution in interval notation.…

A: The objective of this question is to find the point of intersection of the two given lines y₁ =7x+…

Q: x-17 Find the area bounded by y = x²-3x-54 (Round the answer to four decimal places.) , x = 2, x =…

A: The area bounded by the curve y=x3−3x−54x−17​ is approximately 0.7868.Explanation:Evaluate the…

Q: This exercise is based on the following table, which lists interest rates on long-term investments…

A: The objective of this question is to find out how long it will take for an investment of $9,000 to…

Q: Find the maximum and minimum values of the function g(theta)=8theta-9sin(theta) on the interval 0,…

A: local minima and global minima is (0.4579, -0.3160)no local maximaglobal maxima (1.5708,…

Q: show all steps please! thank you!

A: Given position function with respect to time for particle 1s1​=4t−t2 -----(1)The position function…

Q: Find the average rate of change for the following function. f(x) = 4√√x between x = 1 and x = 9 The…

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Q: Q1 C7

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Q: In this problem you will calculate the area between f(x)=2x^2 and the x-axis over the interval [0,5]…

A: The objective of this question is to calculate the area under the curve f(x) = 2x^2 from x = 0 to x…

Q: 8. Find all necessary information and sketch the graph for each of the following. ст 5 a) f(x) =…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Consider the function f(x)=10 root x +10 on the interval [2,5]. Find the average or mean slope of…

A: Therefore, the required answers are a) The average slope is m=310​(5​−2​)=2.739514717088982158b)…

Q: Q Let x)=x+2x-8. For what value(s) of x does f(x) have a local minimum? Paragraph V B I UA Ev Ev

A: The objective of this question is to find the value of x at which the function f(x) = x^2 + 2x - 8…

Q: At a price of x dollars, the supply function for a music player is q = 95e0.006, where q is in…

A: we will find the marginal supply and given parts.

Q: An ice cream cone can be modeled by the region bounded by thehemisphere z = √8 − x2 − y2 and the…

A: (a) Sketching the ice cream cone in 3 dimensions:The hemisphere z=8−x2−y2​ represents the upper half…

Q: Precalculus Question (8)

A: a. (0,B2)b. (0,FC​)Explanation:For both numbers, the y - intercept is a point at the given when x=0.…

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Q: When pineapple juice is left standing, it settles so that it thickens toward the bottom. Suppose a…

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Q: Please can you help me witht he diferential geometry question I'm finding quite difficult

A: Step 1: Step 2: Step 3: Step 4:

Q: Let C denote the following disconnected surface: C={(x, y, z) = R³ | x²+ y²=1Ux²+ y² = 4, −1<z<1}.…

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Q: [3] (a) Evaluate dx (b) Determine if the following integrals are convergent or divergent. Evaluate…

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Q: 7. Given: sin(x)= ½, sin(y)= ½ and 0<x,y< π <? find the value of the following 2 expression:…

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Q: Evaluate the following limits: a) lim 20 7-6 10r2 r-4 b) lim q-3-79-6 qco 2q4+4q-3-10q-8 c) lim…

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Q: lim n-α (+)

A: We solve this limit by using L' Hospital rule.