In section 5.8, we saw that f1 du = tan ¹(u) + C. Use algebra, a u-substitution, then this formula to compute ✓ 12,² +3 dr. Show all of your work, including what you choose for u and how you find du.

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A: To find the points at which the helix  intersect the sphere .

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A: To find .

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A: Let . To find the following.

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Q: then A-¹ = A = [ 3² ],

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Q: 1. Sketch one cycle of the following trigonometric equation, y = −2 sin(3x – 180°) + 1.

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Q: 3x x-∞0 px+7 a) lim- = 2

A: (a) Gven,

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Q: If r(t) = cos(-5t)i computer' (t) = + sin(−5t)j + Ok i+i+ k k+C and fr(t) dt = with C a constant…

A: we are given a vector function and we need to compute its derivative and integration.

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Q: Show algebraically that ƒ(x) = |x − 1| = x = 1. J−x+1 x≤1 (x - 1 x > 1 is not differentiable at

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A: given

Q: If f(x) = 5 arctan(3x), find f'(x). Find f'(4). f'(4) = 5500 VER

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Q: Ex 3. Use the graph of f in the figure to find the following values or state that they do not exist.…

A: Given: To Find: To find the following:

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A: The base of an aquarium with given volume V is made of slate and the sides are of glass. If slate…

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Q: (a) Suppose that a reservoir supplies water to an industrial park at a constant rate of r = 4…

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Q: True Or false, and justify answer: Given h(x)=x²-1 + 2TT -f(x), where a is a 2πn (x^-I-f'(x) x-n…

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Q: The proper angle for a ladder is about 75∘ from the ground. Suppose you have a 29 foot ladder. How…

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Q: 1 a cos x + b sin x + c a, b, c > 0, c> a, c + a c - a dx 9 where b с a 2

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Q: We want to build a cylindrical tank with a volume of 216 m^3. The tank has no lid and the material…

A: We want to build a cylindrical tank with a volume of 216 m3. The tank has no lid and the material…

Q: -10 4,0 6,sqrt(28)) f(x)=√√√5x - 2 compute the instantaneous slope at: (6, √28) Start with two…

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A: Explanation of the ans is as follows

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A: Consider the given figure below:

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Q: For Exercises 10, use a graphing utility to graph the polar equation and describe the graph in a…

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Q: The position of a particle is give by s=f(t)=6t^3+4t+9 Find the velocity and the acceleration

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Q: Find the equation of the plane which passes through O and is parallel y+z= x+ (3x + y) = 6

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A: The given function is The Taylor series of  at

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A: Evaluate and simplify .

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Q: S x³ – x² x¹ + 2x² + 1 хр

A: To give a detailed solution for this integral by using partial fraction decomposition.