4. A curve is given by the equation y = e (* +1). Find the asymptotes (if exist), the intervals of increase/decrease, the intervals of concavity and hence trace the curve.

Q: The tangent line to the graph of y = h(x) at the point ( -1, 4) passes through the point (3, 6).Find…

A:

Q: State the period of y = 5 csc (x) and sketch its graph over two full periods. Be sure to label all…

A: The interval for which a graph completes its one cycle is called the period of the function.  The…

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -5 and g'(3) = 2.…

A: Here, y = g(x)  and g(3) = -5 i.e. when x1 = 3, then  y1 = -5 and g(3)=2 i.e. At x =3, the slope, m…

Q: 1. Sketch the curve by following the guidelines: a) domain, b) intercepts, c) symmetry, d)…

A: Domain set of all input values where function defined Range set of all output values

Q: 3. Sketch a graph of the position of an object that has an average velocity of • -5 mph for times…

A: As we know the rate of change of position  is velocity let object is moving in x direction hence…

Q: 1 . Find the point on the graph of 1+ x where the tangent line has the greatest slope.

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Q: Find the orthogonal trajectories for the family of curves. Use a graphing utility to graph several…

A: The equation for family of curves is y2=Cx3 . So the value of C is equal to y2x3 . According to…

Q: 9. Find the family of the curve whose slope at any point is V√x + √x and also the member which…

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Q: Find the asymptote(s) of the given curve. 31 2x

A: The given curve is y=x2-32x-2. Vertical Asymptote: A vertical asymptote for a function f(x) is a…

Q: За — 5 The graph y = has a horizontal tangent at x = et

A: Tangent to the curve at x = a is horizontal if slope at x = a is 0

Q: 28. The line tangent to the graph of g at the point (x, y) inter- sects the x-axis at the point…

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Q: Graph the curves ina. Where do the graphs appear to have vertical tangent lines? b. Confirm your…

A: Now the graph is, From the graph, the tangent line is appears to be vertical at x = 0.

Q: The tangent line to the graph of y = h(x) at the point (-1, 7) passes through the point (5, 4). Find…

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Q: The tangent line to the graph of y g(x) at the point (4, 2) passes through the point (1, 4). Find…

A: Tangent line to graph g(x) at a point (4,2)⇒(4,2) is point on g(x)g(4)=2

Q: Let P(t) be the population of a bacteria culture after t days and suppose that P(t) has the line y =…

A:

Q: The tangent line to the graph of y = g(x) at the point (4, 5) passes through the point (7, 0). Find…

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Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: Find the slope of the tangent line that passes through point (1, 2) to the graph 8y³ + x²y O-2/97…

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Q: Suppose a curve is defined by the equati on y2 = x*(2- x). What is the equation of the line tangent…

A: Given curve

Q: For the curve y = ax + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: we have to solve the problem

Q: Find the equation of the tangent line to the graph of x4y16=1 at the point (81,1/3) and at the…

A: We use slope point form to equation of tangent line.

Q: 2. Find the equation of the horizontal asympto

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Q: How can we find the horizontal and vertical asymptotes of the curve?

A: We find the horizontal and vertical asymptotes of the curve

Q: 12. If a graph is concave up on an interval, what happens to the slope of the tangent as you move…

A: The objective is to explain that if a graph is concave up on a interval, what happens to the slope…

Q: 4. Find the member of the curve whose slope at any point is and passes through the point (3, 4)

A: Given slope (m) = 3x/4y Passing through a point (3,4) Therefore member of the curve whose slope…

Q: find the Po s at which the tang ent liae to the graph of funstion S)= x3-4x+ 5o has Slope equalta 30

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Q: 1 Find the two points on the curve y=- at which the tangents have as slope of -.

A: Given,            The curve y=1x at which the tangents have as slope of -12.To find : The two points…

Q: of X メ curve Finu ん terms passes thrOush 11っの)

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Q: 4) Find a formula for the line tangent to the curve at the point (4,4).

A:

Q: The graph of y = f(x) (solid) and its tangent line at (0, - 5) (dashed) is shown. 10+ 6- 4- 10 -9 -8…

A: Given: The graph of y=f(x) and its tangent line is at (0,-5) (dashed) is shown.

Q: Find an equation for the tangent line to the curve n = 4- 2 at (-1,3).

A:

Q: The slope of the line tangent to the graph ofy= xe^ at x =In 2 is A 2 In 2 2 In 2+2 B.

A:

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = -4 and g'(2) = 5.…

A: Given function is                                              y=g(x), at x=2g(2)=-4 and g'(2)=5 we…

Q: a) Calculate the length of the curve defined by x = -3 )on the interval 1 sys9.

A: (a) Given that, x = 13 y (y-3) on the interval 1 ≤ y ≤ 9   We have to calculate the length of the…

Q: Graph the curves ina. Where do the graphs appear to have vertical tangent lines? b. Confirm your…

A: Given: x23-x-113 To Find: a. Where the graph appears to have Vertical Tangent Line.b. Confirm your…

Q: Find the exact length of the curve over the given interval. 4 3/2 X= 3 1sys4

A: Given curve is x=43y32, 1≤y≤4

Q: The tangent line to the graph of y = g(x) at the point (6, 4) passes through the point (2, 9). Find…

A: The tangent line to the graph y=g(x) at the point (6,4) passes through the point (2,9). Note:…

Q: 5.) Assume that the given graph gives the position function of a particle which is moving along a…

A: Consider the given graph showing the position function of a particle which is moving along a…

Q: 9. Find the maximum and minimum values of the following curve:

A: To find the maximum and minimum values of the given curve, first we find the critical points.To find…

Q: Let k (x) = 2x and consider its graph. %3D Find the slope of the secant line of this curve…

A: A secant line is a straight line joining two points on a function. It is also equivalent to the…

Q: Problem 20 To find the length of the curve defined by y=(2x^4)+9x from the point (-3,135) to the…

A: length of the curve defined by y=(2x4)+9x from x=-3 to x=3 is given by  So, we find dy/dx

Q: 7. An equation of the line tangent to the graph of f at the point (2, 7) is y = 4x – 1. Find f(2)…

A: Topic - point of tangent To the curve and slope of tangent to the curve

Q: 2. Find the slope of the curve y 3x +1 at the point (-0). Draw the graph of the curve. KIVERSIT TLOU

A: Solution:Giveny2=3x+1  at -13,0To find Slope of the curve and Draw a graph of the…

Q: What is the slope of the tangent line that touches the graph of In(y) + eA-=3y-4x at the point 3. 5

A:

Q: Find the slope of the tangent line to the graph at the given point. (x2 + 4)y 8, (2, 1) Witch of…

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Q: The horizontal asymptotes of the curve 12x y = (zª + 1)'/ are given by Y1 = and Y2 = where yı > Y2-

A: Asymptotes are the tangents where the function tends to meet at the extremities of the x and y axes

Q: The tangent line to the graph of y = g(x) at the point (6, 8) passes through the point (3, 2). Find…

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Q: of the asclength /3 Curve Find the for 2 x 3.

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Q: 2)a) Sketch a single graph that is only increasing and only concave down.

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Q: 3. If the graph of y=fcx) has a horizontal tangent at x=a, what is happening at this point ? I…

A: For a function ; a point is considered. A horizontal tangent exists at this point which means that…