Find the limit and determine if the function is continuous at the point being approached.

Q: Use the following information to complete parts a. and b. below. f(x) = (1+x) -1/5 ; approximate…

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Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

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Q: (a) Estimate the area under the graph of the function f(x) = subintervals and right endpoints. Round…

A: The given function is fx=1x+7 from x=0 to x=1

Q: Use the Divergence Theorem to evaluate F. ÑdS where F(x, y, z)=x²i +2y²j+z²k S and the surface S is…

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Q: The route that a trolley takes around a city can be represented by the functions x² + y² = 5. A…

A: To find out the location means the points where the trolley meet the train.

Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: Topic = Derivative

Q: Find the market equilibrium point for the following equations: Supply: .10x + 5 Demand: -.15x + 10

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Q: Use linear approximation, i.e. the tangent line, to approximate √25.4 as follows: Let f(x)=√. Find…

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Q: Question 14 Each side of a square is increasing at a rate 3 in/s. At what rate is the area of the…

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Q: Solve each of the equations for 0≤x<2. sin.x = 37. sin. TRIGONOMETRIC EQUATIONS 39. 4 sin²x = 3…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: 30. A trough has ends shaped like isosceles triangles, with width 3 m and height 4 m, and the trough…

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Q: es and state values of 0 that produce the entire graph s the entire graph of the parabola?

A: We have to convert in polar form from the given Cartesian curve (parabola)

Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 25. [][₂₁x² +…

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Q: y = √√x S 0 10 5t cos (¹0) de dt

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Q: 4. If = tanx, show that the relation y' = 1 + tan²x.

A: Let's solve.

Q: (b) Show that the following sequence is convergent: 1+ (-1)" n² Yn = √2+ (c) Show that (yn)neN is…

A: A Sequence &lt;an&gt; is convergent if and only if limn→∞ an is finite and unique.

Q: a) Determine the continuity of f(z) at z=2i where z² +4 f(z)={z-2i z - 2i, if z # 2i, if z = 2i.

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Q: Consider the function f(x) = 12x³ + 60x¹100x³ +5. For this function there are four important…

A: Here we have to find the extrema.

Q: Find an equation for the hyperbola described. Graph the equation Center at (-5,-4); focus at…

A: We need to find equation of hyperbola.

Q: 0px + xp (xxx)

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Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: below

A: We have to choose the correct option from the given options according to the given graph of line

Q: Slope

A: We know that, A function, in mathematics, an expression, rule, or law that defines a relationship…

Q: Use the Divergence Test to determine whether the following series diverges or state that the test is…

A: Divergence Test for Series : Consider the series ∑n=1∞ an .If limn→∞ an is non zero or does not…

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: Solve 3 sin(2x) - 4 sin(x) = 0 for all solutions 0 < x < 2π x= Give your answers accurate to at…

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Q: A population of 450 bacteria is introduced into a culture and grows in number according to the…

A: Given, p(t)=4505+4t73+t2

Q: Find the average value of f(x, y) = x² y over the rectangle R with vertices (−3, 0), (−3, 8), (2,…

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Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. an = tan…

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Q: I = 3/√/2 6.³ 0 /9-y² Ivo e³x²+3y² dx dy y

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Q: A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7…

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Q: Using polar coordinates, evaluate the integral Se sin(x² + y²)dA where R is the region 4 ≤ x² + y² ≤…

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Q: `11,  Find a function  f(n)  that identifies the nth term  an  of the recursively defined sequence,…

A: The solution is given below

Q: 35) Given the acceleration, initial velocity, and initial position of a body moving along a…

A: 35) Given:     Acceleration a=18cos 4t    Initial velocity v0=2   Initial position  s0=-7…

Q: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: 5. S √x²-a² dx

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Q: Find an antiderivative F(x) with F'(x) = ƒ (x) = 11+ 15x² +14x6 and F (1) = 0. Remember to include a…

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Q: 23) (-4,-24) 30- 20+ 10+ to.p -10+ -20- f(x) = x3 + x² - 6x -30 (3, 18) 2 Find the area enclosed by…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1. Determine the value of a so that A= 2i +aj +k and B= 4i-2j-2k are perpendicular a. 1 unit b. 2…

A: 1. Determine the value of a so that A= 2i +aj +k and B= 4i-2j-2k are perpendicular. We have, A= 2i…

Q: Determine the appropriate rotation formulas to use so that the new equation does not contain any…

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Q: Find the maximum value of the parabola using the following equation: f(x)=-x^2+4x+3

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Q: A rancher wants to fence in an area of 500,000 square feet in a rectangular field and then divide it…

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Q: ← A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet…

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Q: A company that produces cell phones has a cost function of C = 20x² - 541x + 22940, where C' is the…

A: This question can be solved using the concept of maxima and minima.

Q: Solve the initial value problem. dr-csc² 50 cot 50, 42) de 43) dy dx 3 (7) - y(0) = 6 (6 + x)2'. = 3

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Q: Water is leaking out of an inverted conical tank at a rate of 14000 cubic centimeters per min at the…

A: Given that, the leakage rate is 14000 cubic centimeter, the height of the tank is 12 meters and…

Q: dr Let A be the area of a circle with radius r. If dt 5, find dA dt when r = 4.

A: We will find the required.

Q: TRUE or FALSE: If a skater is skating directly away from a 6 meter tall lamp at 7 meters per second,…

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Q: 6) y = (4 - x2/3) 3/2 from x = 1 to x = 8

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Q: Given f''(x) = - 16 sin(4x) and f'(0) Find f ¹ƒ(3/3) = = 6 and f(0) = - 5.

A: SOLUTION-