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Q: Find the derivative of H when and H(x) = (f(x))² – (g(x))² f'(x) = 8 g(x), g'(x) = 5 f(x). 1. H'(x)…

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Q: Sodium chlorate crystals are easy to grow in the shape of a cube by allowing a solution of water and…

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Q: If y = y(x) is defined implicitly by 3y² + xy + 2 = 0, find the value of dy/dx at the point (5, -1).…

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Q: 25. S tan¹x secºx dx

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Q: The tank in the form of a right-circular cone of radius 8 feet and height 15 feet standing on its…

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Q: the answer came out to be arccos(-1/-10)/1 Could you explain this to me?

A: Given that,fx=x-10sinxWe need to find the least positive value of x for which f has a horizontal…

Q: If No - My M equation = Q, where is a function of y only, then the differential has an integrating…

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Q: If f and g are functions that satisfy f'(2) = -3 and g'(2) = -1, find h'(2) for h(x) = -5f(x) +…

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Q: Calculus is a powerful tool used in all areas of physics. One of the initial applications areas is…

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Q: 2. Find v and a if r = b(1 + sin t) 0 = et - 1

A: r=b(1+sint)θ=e-t-1we know  v=wrw=dθdtd dθ(eθ)=eθd dθ(sinθ)=cosθ

Q: The demand for a product is given, for p, q ≥ 0, by p = f(q) = 45 -0.04q² (a) Find the p- and…

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Q: A group of engineers are building a parabolic satellite dish whose shape will be formed by rotating…

A: We have to slove above question

Q: y = log₂ (sec(x))

A: Given query is to find the derivative.

Q: Find f'(x) when f(x) = 2 sec²r + tan² r. 1. f'(x) 6 tan² secx 2. f'(x) 2 sec²r tan r 3. f'(x) = 6…

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Q: == 3x²y+y³-12x-15y +3

A: Given :fx,y=z=3x2y+y3-12x-15y+3

Q: Find the general solution of the differential equation. Then, use the initial condition to find the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 2 dy 3x²-x-5 dx (x + 1)(y + 1)' .y(1) = 4

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Q: 10. x = (y-2)², y = x about y=-1

A: Solution is given below:

Q: The function f has a removable discontinuity at x=7, then which of the following statements must be…

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Q: Find an equation for the tangent line to the graph of f(x) = 2 sin(sin(x)) at the point P(, f(T)).…

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Q: 3 Assuming -x³+4y²-5xy = 0 defines y as a differentiable function of x, use the theorem dx 11 dy to…

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Q: 37–38 Find equations of the tangent line and normal line to the given curve at the specified point.…

A: The given equation of the curve is: y=3x1+5x2 Find the equation of the tangent line at the given…

Q: An object is thrown upward at time t = 0. After t seconds, its height is y = -4.9t² + 5t+5 meters…

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Q: Explain why Newton’s method fails to find the root of x^3 − 3x + 6 if our initial guess is x1 = 1.

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Q: If f(x) is a constant function, then f'(x) is zero. True False

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Q: The charcoal from a tree killed in the volcanic eruption that formed a crater contained 31.5% of the…

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Q: a. Use implicit differentiation to find the derivative b. Find the slope of the curve at the given…

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Q: Draw a dependency diagram, and write a chain rule formula for dt where z=f(p.q). p=g(t), q=h(t).

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Q: Hello, can you please walk me through the derivative of (dy/dx): y=(arctan(x))2 Keeping the answer…

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Q: X-4 x2-5x+4 Let f(x) = (a) limx→ 4 f(x) (b) limx→ 1+ f(x) (c) limx→ ∞ f (x) Find

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Q: An object moves along the y axis (scale in feet) so that at time x (in seconds) it is at f(x) = -5x²…

A: To find at what time velocity will be 0.

Q: 1. Determine whether the sequence converges or diverges. If it converges, find the limit a. an =…

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Q: Find the indefinite integral. Include a multiplication sign between functions. For example, z. e².…

A: B=∫10e2zdz∫ezdz=ez+c

Q: z(x, y) = 5x² - 2xy + 2y²-18y-2

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Q: dM 1. The rate at which a quantity M changes is given by = t² +7.If M(1) = 4, find M(t). dt

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Q: Find the first derivative 3 the function x²y + y² = 40 implicitly for

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Q: 4 solute minimum value of f(x) = 2x² - 4x such answer exists. IMAL PLACES.)

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Q: Use the integral test to determine the convergence c divergence of the series k=1 7 4k+ 2

A: Given: ∑k=1∞ 74k+2

Q: 3 3. Find the value of the definite integral: So 2 7t² + 10t - 1 t3+3t²-t-3 dt

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Q: t the vectors [3,-

A: We know that , Dot product of two perpendicular vectors is zero.

Q: Determine the location and value of the absolute extreme values off on the given interval, if they…

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Q: Find the indicated partial derivatives A) f(x,y) = arctan(y/x), fx(2, 2) B) f(x,y) =…

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Q: 1. Determine the following, if g = [3, -2,5] and h = [4, 1, −6]. a) g + h b) g - h c) g.h d) Igl

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Q: e) g'(x) if g(x) = e3x+5 6 4 e2x + e²

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Q: Solve the given differential equation. All solutions should be found. x - 2y X dy dx NOTE: Use c for…

A: The given differential equation is: dydx=x9-2yx  To solve the given differential equation.

Q: The function f(x,y) = xy² – 2x² – 4y²2 has critical points (0,0), (4,—4), and (4,4). Which of the…

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Q: 11. Together, the curves y = e, y = 5, and x = -2 enclose exactly one region. Determine the area of…

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Q: Find all points on the graph of the function f(x) = 2 sin(x) + sin²(x) at which the tangent line is…

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Q: 1. Given two vectors, a = nearest degree. [1, 2, 4] and b = [− 6, 0, 3] determine the angle between…

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Q: Find the derivative g(t) of the function using the definition of derivative. 5 √t

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