Differentiate. f(x) = In f'(x) = X 6

Q: 2) Determine whether the sequence is convergent or divergent. If it is convergent, find its limit…

A: To determine whether the sequence is convergent or divergent. If it is convergent, then to find its…

Q: The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does…

A: The graphs of f and g are given. Use them to evaluate each limit, if it exists.(If an answer does…

Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 15 m/s, its height…

A:

Q: 2. On what intervals is the function increasing and decreasing? On what intervals is the function…

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Q: (c) h(y) = 754 h'(y) = * ( = 7 (5(~²))* = 7 @y= √√x + √x + √ (d) dy dx

A: The given function,

Q: The side of a square is measured to be 10 ft, with a possible error of ± 0.4 ft. Enter the exact…

A: The side of a square is 10 ft., with a possible error of 0.4 ft.

Q: Given F(r, s, t) = -r (3s5 + 6t5), compute: Frst

A:

Q: An ant who is crawling on the ground has its position at time t (in seconds) given by t y(t) = 2+…

A: Given that an ant who is crawling on the ground has its position on time t is given by

Q: Calculate the derivative of the following functions. 15 (a) f(x) = (1) f'(x) = (b) y = dy dt h'(y) =…

A:

Q: Match each trigonometric function with its derivative. Enter the correct letter in the box beside…

A: Given, (A)

Q: Find the derivative of the following function. 8 9 f(w) = ³ + xw²+6w+5 5 f'(w) =

A: Given,

Q: Write a polynomial f(x) that satisfies the given conditions. Degree 3 polynomial with integer…

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Q: Use logarithmic properties to find the exact value of log17 (175).

A:

Q: Find the following derivatives. z and Z₁, where z = 6xy - 4x²y, x = 5s + t, and y = 5s - t Zs (Type…

A:

Q: Find the mass of the one-dimensional object. A wire that is 5 ft long (starting at x = function of…

A: Give that a wire of length  whose density function is  We have to find the mass of the object.

Q: 4. Find the following limits. If the limit does not exist, write DNE and explain why. If the limit…

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Q: How much work is done lifting a 15 pound object from the ground to the top of a 30 foot building if…

A:

Q: Find the first partial derivatives of the following function. f(x,y) = 3xy³ + 1 =

A: By treating one variable at a time and other as a constant, we can find the partial derivative.

Q: Find the exact length of the curve. 36y² = (x² - 4)³, 2≤x≤6, y 20

A: Find the exact length of the curve.36y2=(x2−4)3,2≤x≤6,y≥0

Q: 7. Find the first quadrant point on the curve y=x²-3x² at which the tangent to the curve is parallel…

A:

Q: Determine the derivative for each of the following equations. dy dr a.y=sin (8 x) ⇒ b.y = 8 cos (z)…

A: (a) y=sin⁡(8x)

Q: Find d37 -(sin x). dx37 Derivative:

A:

Q: A particle moves according to a law of motion s= = tª — 2t² + 1, t > 0, where t is measured in…

A:

Q: Use properties of exponential functions to solve each equations. Show all steps and give the exact…

A: The given equations (a) (b)

Q: It is given to you that an equation of the tangent line to the graph of y= g(x) at x= 9 is 4x+10y=…

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Q: K What is the slope of the line tangent to the graph of y=tan(-x) at x = - 4? The slope of the…

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Q: Concavity and points of inflection. Answer the following questions using the function f(x) The…

A: The given function .The aim is to find the concavity intervals of the given function.

Q: es of x in the interval [0,2ë] at which the graph 0 as a horizontal tangent.

A:

Q: The function f(x) = −2x³ – 19.08x² +70.179x - 3.59 is increasing on the open interval ( ). It is…

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Q: Find the following limits. 1/x² COS X cos 2x (a) lim ( x →0

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Q: Find the point where the tangent line to y = 5x² at x = 0.7 crosses the x-axis. x-intercept =

A:

Q: 5. Find the equation of the ellipse with center at (4, 4), vertices at (4, 10) and (4, -2), foci at…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Consider the following equation. x²7xy-y²-5y = -47

A: x2−7xy−y2−5y=−47

Q: Compute the following values for the given function. f(x, y) = 8x² + 5xy - 9x + 4. f(1, 2) = f(2, 1)…

A: Given,

Q: Suppose that the number P(t) of bacteria in a culture after t days is given by the formula P(t)=34…

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Q: Use the Chain Rule to find dz dt 1 where z = 3x siny, x = t², and y = 2t4.

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Q: Sketch the region bounded by the curves. Find the exact coordinates of the centroid. y=e¹, y=0, x=0,…

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Q: Use the FOIL method to find the indicated product. (9x - 72) (3x - 7z)

A: By using the FOIL method to find the following product.

Q: Given the function f(x) = 7x+3 - 9e Determine the equation of the tangent line at the point (0, -6).

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Q: Find the smallest number n of terms needed to obtain an x 9 approximation of the series accurate to…

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Q: A tank contains 1140 L of pure water. Solution that contains 0.03 kg of sugar per liter enters the…

A: The tank has 1140 L of pure water.Solution has 0.03 kg of sugar per liter enters the tank at 3 L/min

Q: The graph below shows a function f. Select the correct signs for each of f, f' and f" at each marked…

A: The given graph

Q: Find the volume of the given solid. Enclosed by the paraboloid Z = 5x2 + 4y2 and the planes x = 0, y…

A: The region enclosed by planes

Q: Find dy dx xy + y² = 5 dy-0

A:

Q: 7. The equation of motion for a particle is s(t) = t4 – 2t³ - 20t² +20, t≥ 0 where s is in meters…

A: Velocity is the derivative of the position function with respect to time. So, we need to find the…

Q: 2. Does the following function satisfy the preconditions of the Mean Value Theorem on the given…

A: Mean value theorem states that for a continuous and differentiable function f(x) on the interval…

Q: Write the given expression as a SINGLE logarithmic term. log(x + 6) - / log(x + 3) + log(x - 1), x>…

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Q: Let f'(x) = 12x5 lnx + 2x³ f'(e²) = f(x) = 2x6 ln x

A: given here f(x) and asked to find f'( e2 ).

Q: Find the area between the curves. y=x2 − 9x + 3  and  y=x2 + 9  from  x=0  to  x=6

A: The region between the curves  from The graph of region

Q: Let F(x) = f(xf (x²)). Suppose that ƒ(4) = 6, ƒ'(4) = 1, and ƒ'(12) = 5. Find F'(2).

A: Given, .Given,  f(4)=6, f'(4)=1 and f'(12)=5.