1) Find the egin of the tangent I normal line to the graph y y=√x-1 at the point (3,2) 100

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A: For given graph for (-∞,0) slope is positive but decreasing.   ( cancel out option 4)at x = 0, slope…

Q: (Hint: Rationalize twice) (ii) Use the result of part (i) to evaluate lim #42 (Hint: It's a one line…

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Q: QUESTION 1 Find the specified domain. For g(x)=√√x + 6 and h(x) = O [-6, 9) U (9,00) O [0, 75) u…

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Q: Find three positive real numbers whose sum is 75 and whose product is a maximum. Enter the three…

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Q: The graph below is the function f(x). -5 k 5. -3 -2 -1 432 12445 -2 -4 ● a 4 a Find the following.…

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Q: Find all Where bothe the values of X the tangent horizontal 3 2 X²³ - 3x²³² - 8x +14 23 line 13

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Q: Find the area of the region between the graphs of f(x) = 9x + 8 and g(x) = x² + 6x + 2 over [0, 2].…

A: From the given curves the bounded region is shown below. Now taking the vertical strip, so the area…

Q: TOPIC 2: Derivatives of Logarithmic Functions (ba Basic Rules: (In x)': a) f(x)=- +2 In(x) 2 X .…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: -5 -4 -3 -2 -1 5- 4 3 2 1 -2 -3 * 2 3 4 5 Use the graph of f(x) above to estimate the value of f'(0)…

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

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: The given function, fx=11-2xif x<2x2-xif x≥2. We have to find the limit of the function at x=2.

Q: Find the indefinite integral. Remember to include a "+ C" if appropriate. Enclose arguments of…

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Q: 1. 2" Find the first five terms of the infinite sequence whose nth term is a₁= · 3" +1 work. Write…

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Q: 4 If ſ₁ ƒ(x) dx = 12, then ¹ f(4x) dx is equal to If ſ¹ ƒ(x) dx = 12, then fx f(x²) dx is equal to

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Q: termine the interval on which f(x) = is continuous. Classify any discontinuities.

A: Given query is to find the interval where function is continuously.

Q: determine the open intervals on which the graph of the function is concave upward or concave…

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Q: could you clarify part a please ? is that a g? or a 9? what is part a answer??

A: Given that f(x)=x2-5x-14x-7we have to find limx→7f(x)

Q: Let ƒ(x) = |x − 3). Evaluate the following limits. ƒ(x) — ƒ(3) x-3 lim x→3- lim x→3+ f(x) — ƒ(3) x-3…

A: Topic = Function

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Q: The population of a city can be modeled by P(t) = 10e0.04t thousand persons, where t is the number…

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Q: Due to changes in the environment the fraction of the population in Artemis (fictional) with…

A: see below the answer and calculation

Q: Determine the exact solutions for x on the interval [0,2π). sin² x = sinx • cosx.

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Q: Textbook Estimate the limit numerically or state that the limit does not exist: In(2x + 7) - ln (7)…

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Q: Find lim h→0 lim h→0 f(3+h)-f(3) h f(3+h)-f(3) h || - if f(x)=x² +2. (Simplify your answer.)

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Q: Let f(x) = ln(2e + 3). Then f-¹(x) equals None of the above 2/ln(e* - 3) In(e* - 3) In(e* - 3) In…

A: Note: Since, the student has posted two questions but the second question is incomplete. So, we are…

Q: 3. Write the first five terms of the sequence given by an = (-1)" (2n + 1). Show all work. Write…

A: given  an=(-1)n(2n+1)for a1, put n=1

Q: Evaluate the integral. 8 6.² - xex Jo (1 + x)² dx

A: integration by part is given by∫fdg=fg-∫gdf

Q: Find the derivative of the function. 3 g(x) = ² + 3 +9√√x g'(x) =

A: g'(x)=ddx3x4+2x2+9x3

Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given…

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Q: . Sketch a graph that satisfies the following properties. • limx→2+ f(x) = 4 ● limx→2- f(x) = 3 •…

A: Given query is to find sketch the graph with Indicated properties.

Q: Which one of the following is NOT a separable first-order differential equation? A x 2-52²-1 dy ay…

A: Find which equation is not separable.

Q: If the cost function for a commodity is C(x) = ³ + 2x² + 2x + 12 dollars 90 find the marginal cost…

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Q: Which one of the following is the general solution of 3 + 5y = 1? dz y=+cel -+ce where CER ++ where…

A: To find the general solution of given differential equation

Q: Graph the function. [xl if x s1 x² if x>1 f(x) = ZV

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Q: Evaluate the integral. π/6 T -π/6 π/6 - π/6 [(2 sin t)i + (1+4 cos t)j + ( sec² t) k] dt = [(2 sin…

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Q: Estimate the limit numerically or state that the limit does not exist: 10² Give your answer to at…

A: limx→ 010x-1x=limx→ 0ln10· 10x1Plug in the value x=0.=ln10· 1001=ln10

Q: Find the indicated derivative. If f(x) = √√x+2, find F"(x).

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Q: Which of the following is a consequence of the Intermediate Value Theorem without further…

A: Given f is a continuous function on -2,8 such that f-2=-1 and f8=7 , The Intermediate Value…

Q: The graph below is the function f(x) DO 8 4 Find lim f(x) I-1- Find lim f(x) Z-1+ Find lim f(x) HI…

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Q: Solve the equation. In x+ In 2x=4

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Q: 2. d. Explain the difference between f(a+h)-f(a) h and lim h→0 f(a+ a+h)-f(a) h Use the definition…

A: Please see the below picture for detailed solution.

Q: Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use…

A: Given Graph:-

Q: QUESTION 2 Write an inequality of the form |x-a k so that the inequality has the given solution…

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Q: Use the indicated substitution to evaluate the integral. S (Give your answer to three decimal…

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Q: Suppose an arrow is shot upward on the moon with a velocity of 49 m/s, then its height in meters…

A: Given height function h( t ) = 49t - 0.83t2

Q: Let f(x) = 1- 8x + 4x². Calculate the following values: f(a)= 4a²-8a+1 f(a+h) = 4a²+ Sah+ 4h²-8a-8h…

A: To find the value of difference quotient.

Q: Evaluate the integral using Integration by Parts as a first step. sin -1 (x) 5x² dx (Express numbers…

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Q: Find the horizontal and vertical asymptotes of f(x). 3x X+4 f(x) =

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Q: If sinx+cos x = 1/3, then 18 sin² X -9|=

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Q: For the pair of functions, write the composite function and its derivative in terms of one input…

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Q: If a rock falls from a height of 39 meters on Earth, the height H (in meters) after x seconds is…

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