Find the values of x for which the function is continuous. f(x) 5x2 + 7 7 all x, х # 5 7 O all x, x ± 5 7 all x, х # V5 7 all x, x + – 5 all real numbers

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A: Let's find.

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: find a power series representation for this function?

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A: The objective of the question is evaluate the given function values.

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A: Evaluate arctan(sec ).

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A: Given query is to find the angel between the vectors.

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Q: Question # 14 Rational Expression Reference Q. 15227 The rectangle shown has length 5æ2+ 10x cm and…

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A: Given problem:- ∫ x2 (csc(2x3) (cot(2x3) dx

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A: the given sequence,an=3+5n2n+n2

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Q: 9 Determine whether the series 9. 9. +...+ 9. +... is convergent or 100 1002 1003 100" divergent. If…

A: 9100+91002+91003+.....+9100n+...common ratio:a2a1=a3a2=1100First term: a=9100common ratio:…

Q: 1. Find D„f at P: f(x,y) = sin(8x – 5y); P (5,8)); u=((i)

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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A: We have to find the centroid coordinates.

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A: Topic = Trigonometry

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Q: 4 The line y= -Lx+3 has a perpendicu lar which fangent to the graph of y= (x²-2) (2x+k) at x=-l,…

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Q: Find polar coordinates (r, θ) of the point (1, −2), where r > 0 and 0 ≤ θ < 2π.

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Q: The number c that satisfies the Mean Value Theorem for Integral of the function f(x) = x2 – 5x + 6…

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Q: Let å = - 5i – 43 and b = - 7ỉ + 23. Find ä · 6

A: This question can be solved using the concept of dot product.

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A: Simplify the equation and solve for x for inverse function.

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Q: Consider a triangle ABC like the one below. Suppose that C=121°, a=64, and b=68. (The figure is not…

A: Given C=121°, a=64 and b=68We know cosine rule is…

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A: Given query is to find the derivative.

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Q: Show that la 1 1 1 a 1 - (а + 3)(а - 1)3. - 1)³. %3D 1 1 a 1 1 1 a

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Q: Find the solution of the initial value problem y" + y = 8(t - 2), y (0) = 1, y' (0) = 2.

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Q: Simplify cot(2 arctan 6). -35/37 -35/12 -1/6

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Q: 2" is convergent. The series 2 n=1 h+1

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Q: 100 (x– 6)" X- n = 0

A: Given

Q: Consider the lines defined by the equations {3 : a – 3 = y – 5 = z – 6 and 4(s) = (-2 – 2s, –2s,6 –…

A: Given lines are: l3: x-3=y-5=z-6 l4→s: -2-2s, -2s, 6-2s   We compare l3: x-3=y-5=z-6 or l3:…

Q: 2. The amount of protein in the bloodstream (mg/L) is given below for 30 patients: 1.4 1.8 1.8 1.9…

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Q: Find the Cartesian coordinates of the point (−√2,(5π)/4)

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Q: cos³ x .3 S dx 1+ sinx

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Q: ind, if any, the local maximum and minimum values and the saddle point(s) of the function f(x,y) =…

A: To find, if any, the local maximum and minimum values and the saddle point(s) of the function fx,…