Show that the limit  lim x approaches infinity [(1+x/2-sqrt(1+x)) / x^2] exists and find its value. I have that the Taylor polynomial T2[sqrt(1+x),0] = 1 + (1/2)x -(1/8)x^2. And an expression for the remainder R2(x), sqrt(1+x)=T2(x)+R2(x) = 1/(16sqrt(1+c)^5) x^3.

Q: (5x - 4)² 1) Let f(x) (9x + 16)² The limit as x approaches infinity is

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Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)>0 when…

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Q: t. determine just one horizontal asymptote of f() by computing an appropiorate llmit. f(x)= V4x^+ qx…

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Q: find domain and asymptotes of  fx= x^2+x-2 over x^2-2

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Q: x*+6x3-1 4. Let p(x) = x5 + 3x² – 1 and r(x) = - x²+x-2 a. How many zeros could p(x) have and why?…

A: We have to solve first 3 parts according to the guidelines.

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A: To find the area of the largest rectangle with given corner points.

Q: 77. Show that if f is a quadratic polynomial, then the SDQ at x = a (for any h + 0) is equal to…

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Q: Find lim √√3x² + 3y² -1. (x,y) →(3,1) lim √√3x² + 3y² -1 = (x,y) →(3,1) (Type an exact answer.)

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Q: Show that the real zeros of f(x) = x^4 + 5x^2 + 3x -7 satisfy (a) No real zero is greater than 1.…

A: We have to find the given statement is correct or not.

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A: given, f(x)=(x+4)(x2+4)

Q: Vx? + 100 – 10 lim x² .2

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Q: 7. Let a be a nonzero real number. Evaluate lim o f (x) and lim,→ f(x), where -00 f (x) = a.x° – 3x*…

A: Given problem is :

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Q: Consider the rational function y= 3x^2-9/x^2-7x A) find all the horizontal asymptote of function B)…

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Q: the horigontal asymptote of the given function. x+9 47) g(x) = x2 – 6 A) y= 0 B) y = 1 C)

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

Q: List the possible rational zeros of the function using the Rational Roots Theorem. f(z) = 3x3+ 9x2+…

A: Explanation of the answer is as follows

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Q: 4. Find lim (x² – 9)/(x² – 8x + 15)

A: To find the limit of given function.

Q: The point (3, 7) is a

A: Follow the procedure given below.

Q: describe all the transformtions of the graph y= sqrt(x) to obtain  y = sqrt(2x+6)+5

A: We know that Translation horizontally: (left or right) f (x + k) translates f (x) left or right if…

Q: 3) Given the cubic function f(x) 3 2 x² + 3x² 13x 15. a) Put f(x) in factored form, show your work…

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