Condense the expression to the logarithm of a single quantity. (Assume all variables are positive.) In(y) + In(z)

Q: Find the limit. lim (t i 6 j + t² k) t-5 lim (t i − 6 j + t² k) = i t-5 i+ i j+ i k

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Q: Solve the following equations: a) y√(1-x²)dy + x√√(1- y²)dx=0 dy x(2 ln x+2) b) = dx sin y+y cos y…

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Q: 5. S COS X 2+3sinx dx

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Q: Which statement is true? If f(x) = 7, then the particular anti-derivative of f(x), is 7x + C If f(x)…

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Q: The graph of g consists of two straight lines and a semicircle as shown in the figure. y -20 y =…

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Q: Solve y"+y' + y = 6sin (2x) supo

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Q: QUESTION 4 If you roll a fair 6-sided die 9 times, what is the probability that at least 2 of the…

A: To find the probability.

Q: MY NOTE An open box of maximum volume is to be made from a square piece of material, s = 30 inches…

A: Given: S= 30 inches

Q: Convert the Cartesian equation Z z = 6-√√36-x² - y² into spherical coordinates.

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Q: COSX Let esinx = Soos* f (t) dt and f determine the value of (1/2) f(t) dut and f is a continous…

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Q: 2. Evaluate the following (Express all answer in Rectangular Form): d. √9+ 2i e. 2¹ + ln(2 + i)

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Q: Does the function satisfy the hypotheses of the Mean value there on f(x)=2x²-3x+1, [0, 2] O Yes, it…

A: We have to find the value of c.

Q: A 10,000 litre rainwater tank is to be built in the shape of a cylinder. It must be at most 3 metres…

A: As per our guidelines we can answer only 3 subparts of the given equation. Kindly repost the…

Q: A company has fixed costs of $5,000. Producing 300 items incurrs a total cost of $26,000. (a) Find…

A: Use derivative and average formula for cost ,for evaluating it.

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Find the derivative of f(x) =de 22 Of(x) e (e-2x) ²-e -2x O f'(x)=x²e-2 (-2) O (E) None of these O…

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Q: A particle moves according to the law of motion s = t³ - 7t², t> 0, where t is measured in seconds…

A: In multiple parts question we are advised to answer only first three sub parts .

Q: we have 27ft squared of material to build a box of maximum volume with a square base and no top.…

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Q: Find the limit. lim t→3(t i-4 j + t² k) a z→3(t 1-4 j + P²³ k) = [i i+ Mi + M k

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Q: Determine whether the sequence converges or diverges. If it converges, please compute the limit.…

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Q: Applying the First Derivative Test In Exercises 29-36, (a) find the critical numbers of the function…

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Q: Eliminate the parameter and write the resulting rectangular equation whose graph represents the…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Evualate the vector valued function

Q: Find the points of inflection and discuss the concavity of the graph of the function. x+7 f(x) =…

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Q: 3. f(t) = (tan² t-t²)³ 4. g(x) = eey

A: 3.  Derivative of tan2t-t23

Q: Ordinary differential equation dx/dy = ( x-e-x )/( y+ey )

A: We can solve as follows

Q: Express the function as the sum of a power series by first using partial fractions. (Give your power…

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Q: Solve the following equations: a) y√(1-x²)dy + x√√(1- y²)dx=0 dy x(2 ln x+2) b) = dx sin y+y cos y y…

A: To integrate.

Q: 10. SHOW ALL WORK Verify the following identity:1 (1 - csc²0) (1 + tan²0 ) = tan² an evels to sty…

A: Given;  (1-csc2(theta)) (1+tan2(theta)) =tan2(theta).

Q: 1- Find the area under one arch of y = cos3 x

A: To find the area under the arch we will integrate the given function under the limits of the given…

Q: I need all the integrals of the trigonometric ratios

A: ∫sin x=-cos x+C∫cos x=sin x+C∫tan x =-ln|cosx|+C

Q: 2 6 5 seco SSS p² sin p dp do de 000

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Q: Calculate the following derivative. (Use symbolic notation and fractions where needed.) d6 = dx6 x

A: We have to find the derivative

Q: Find the Taylor series for  f(x)  centered at the given value of a. [Assume that f has a power…

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Q: Find the exact value of the logarithmic expression without using a calculator. (If not possible,…

A: let y = ln(e23) we know that mn = m1n∴y = ln(e2)13

Q: The table gives the values of a function obtained from an experiment. Use them to estimate S² f(x)…

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Q: HOW ALL WORK pand the logarithmic expression using the properties of logarithms: In xy

A: Topic :- algebra

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: :-In an oil refinery, a storage tank contains 200 gal of gasoline that initially has 100 Ib of an…

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Q: Consider the following function. f(x) = 4x2/3 Find f(-8) and f(8). f(-8) = f(8) = Find all values c…

A: Here, the given function is: f(x)=4-x23

Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t) ||³ = r(t) = e³ti + e-tj to find k(t).

A: By using the formula kt=r't×r''tr't3 to find kt.rt=e3t i+e-t j

Q: Determine whether F(x, y) = 4x²y i+ 9xy²j is a conservative vector field. If so, find a potential…

A: Determine whether F(x,y) is a conservative vector??

Q: Find all solutions to the equation. 4 cos 0 = -sin²0+4 Write your answer in radians in terms of ,…

A: cos2 θ +sin2 θ =1 Cosine function takes value in between -1 and 1.

Q: Evaluate the definite integral. NOTE: Enter the exact answer. |ti + t²j||dt

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x² + 60x + 200,…

A: Given problem:- A manufacturer has determined that the total cost C of operating a factory is   C =…

Q: A fence must be built to enclose a rectangular area of 20,000 ft². Fencing material costs $3 per…

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

A: We have to find the value of c.

Q: QUESTION 10 A company finds that it can sell 120 items at a price of $490 each, and sell 440 items…

A: Given: 120 items at a price of $490 each,  440 items at a price of $150 each.

Q: Find r'(t), r"(t), r'(t) ・r"(t), and r'(t) × r"(t). r(t) = 2t2i - 2tj + 0 18k (a) r'(t) (b) r"(t)…

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Q: 3 find the values of az/ax and az/ay xe³+ ye² + 2 lnx-2-3 In 2 = 0, (1, In 2, In 3)

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