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Q: 4. For the given function find the local extrema using the Second Derivative Test. f(x) = x³ – 9x2 +…

A: maxima minima

Q: 2+ 12 40. Find all local extreme values of f(a) The FIRST local extreme value, moving from left to…

A: Find out the maxima and minima.

Q: Čonsider the following equations. 3 f(x) .3 y = 0 X = -4 х3D —1

A: To find the area of the region bounded by the given curves.

Q: "he graph of x(t) = t+ cos t, y(t) =t+ sin t, 0 <t< 2n is shown belov 6 Compute the slope of this…

A: Topic :- application of derivatives  Note :- as per our guideline if more than one question uploaded…

Q: An inverted pyramid is being filled with water at a constant rate of 65 cubic centimeters per…

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Q: derivatives as functions of

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Q: 3 For the given equation f(x) = x³ +a2 %3D 6x + 10

A: f(x)=x^3+3/2x^2-6x+10 f'(x)=d(x^3+3/2x^2-6x+10)dx f'(x)=3x^2+3/2(2x)-6(1)+0 f'(x)=3x^2+3x-6 take…

Q: 19. inside * = 5sin O and outside " =2+sin0

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Q: Problem 37: Convert the following complex numbers from rectangular form to polar form: a. 4+ j3 b.…

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Q: Consider the curve parameterized by a 3t2 15 and y= 2t3 15. Find equations for all tangent lines to…

A: We have to find the tangent to the parametric curve.

Q: 1 mile = 5280 feet I km = 1000m %3D %3D 1m = 100 cm %3D 1L = 1000 ml 1 Calorie = 4184 joules 1…

A: Follow step 2

Q: answer

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Q: 31 + 98.6, where Tis the temperature, in degrees Fahrenheit, at time t, in hours. R+1 The…

A: The temperature T of a person during illness is given by Tt = 3tt2+1+98.6°F…

Q: The slope of the tangent line is

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Q: Solve the system of equations using matrices (row operations). 3z- 3w = - 4 X+ y+ z+ 3w= -1 2x + y-…

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Q: sincxt sintpx)dx -元 -IK 1/0

A: 1π∫-ππsinx sin(px) dxusing property∫-aaf(x) dx= 2∫0af(x) dx ;  f(-x)=f(x)=1π×2∫0πsinx sin(px)…

Q: (1 — 2x)dx

A: Given,  ∫01(1-2x)dx

Q: An object moves with velocity as given in the graph below (in ft/s How far did the object travel…

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Q: To rationalize the denominator of 45 what value should the numerator and denominator be multiplied…

A: We can answer the question as below.

Q: 6/9 Correct Question 8 of 9, Step 1 of 1 Find the total area bounded by the x-axis and the curve y =…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round…

A: Solve the following

Q: Determine the limit of the sequence or state that the sequence diverges. n an = Vn3 + 2 (Use…

A: Given: an=nn3+2 To find:  limn→∞ an limn→∞an=limn→∞nn3+2 Given limit is of ∞∞ form

Q: Determine whether the planes are parallel, perpendicular, or neither. 7x + 28y - 21z = 1, -3x + 6y +…

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Q: Find the area between the loops of the limacon r = 7(1+ 2 cos 0). Area =

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Q: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

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Q: Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

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Q: Use the Divergence Theorem to calculate the surface integral F• ds; that is, calculate the flux of F…

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Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = e"i+etj K(t)

A: We have to find k(t)=?

Q: 5. You are not allowed to use the graphing calculator For the given equation f(x) = x³ – 6x2 +9x- 2…

A: Only 5 solved... According to given   F(x)=x3-6x2+9x-2

Q: Solve the initial value problem (b) y^ prime +2xy+xy^ 4 =0 ; y(0) = 1

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Q: Find the average value of y = sin x between x = 0 to x = π.

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Q: Find the area enclosed by the given curves. Find the area between the curves y = In x and y = In 3x…

A: Solution:

Q: Find the volumes OF the solid generated by revolving the regions bounded by the graph Of the…

A: Volume of revolution

Q: For the function y=JHx +1 + Find: a) The equation of the tang ent liné at X = 2 b) The equation of…

A: Given,            y=4x+1+2xTo find : a The equation of the tangent line at x=2.                b The…

Q: Find the derivative of the function at Po in the direction of u. X-y g(x,y) = Po(- 1,1), u= 12i + 5j…

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Q: 11. A snowball melts so that its surface area decreases at a rate of 0.5 cm/min. Find the rate at…

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Q: Sx³cos3x?dx

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Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: Evaluate | (2x – y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (8, -5) -80

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Q: dx /1 + 6x²

A: We have to find integration.

Q: 2)Consider the parent function y = x^2. For each function below, describe the transformations which…

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Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i+ 11 sin(t)j + tk; t= 2 T() - T N 2.

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Q: Let S be given by x? + y? + z² = 25 and z > 0, oriented downward. (a) Sketch S and dS. Indicate…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 7x, x = 2, x = 5 and y =…

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Q: Suppose that z = f(a, y) is differentiable at the point (1024, 1024) with, (1024, 1024) = 5…

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Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. Enter…

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Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

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Q: if an open box is to be made using a square sheet of tin, 20 inches by 20 inches, by cutting a…

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

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