2x + k The equation of a curve is given by y = (T dx. x+1 It is given that the curve has a turning point at (1, 2). (i) Show that k = --2.

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Q: An equation of the tangent line to a curve at the point (2, 4) is y = x + 2. if at any point (x, y)…

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Q: 5) Given a curve y = f(x) has a tangent line y = 3x - 4 at a point (- 2, 1) and a tangent line y =…

A: Topic  = Derivative As per guidelines , At a time only one question can be answered.

Q: (a) Find an equation of the tangent to the curve y=ex that is parallel to the line x-4y=1. (b) Find…

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Q: Q-5. The velocity of a particle moving along a line is given by v(t) = 4t3 – 3t? at time t,lf the…

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Q: . Find the equation of the tangent line to the curve y=(x-1)^ 5 (x+4)^2  at the point (2,36). The…

A: As our company guidelines we are supposed to do only first question please repost other question as…

Q: Solve for C given the general functions below and the specific point. 9. Find the equation of the…

A: Since:              The given general equation is of the form:…

Q: (a) Find the slope of the curve y = x -7x at the given point P(2, - 6) by finding the limiting value…

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Q: The curve y = f(x) has a y – intercept of 3. The tangent to this curve at the point (x, y) has an x…

A: Based on x and y intercept value we will find out equation of the graph.

Q: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2. if at any point (x, y)…

A: To find the equation of curve

Q: Q-5. The velocity of a particle moving along a line is given by v(t) = 4t° – particle is initially…

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Q: 3. 4 te (-0, 0), solves x' = -2 Show that x(t) = e2t 2 2 -2 and sketch the graph of the (oriented)…

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Q: The curve y = f (x) passes through the point A(1; 2). Each tangent at any point M(x,y) on the curve…

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Q: Q-5. The velocity of a particle moving along a line is given by v(t) = 4t³ – 3t² at time t,lf the 3…

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Q: x² closest to the point (0, 8). 6. Find the point(s) on the curve y =

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Q: (a) Find an equation of the tangent line to the curve y = 14/(1 + e-X) at the point (0, 7). (b)…

A: Tangent line

Q: (a) Find an equation of the tangent to the curve y = ex thatis parallel to the line x- 4y =1 .(b)…

A: given: the equation of the curve is y=ex. we have to find the equation of the tangent to the curve…

Q: Q-5. The velocity of a particle moving along a line is given by v(t) = 4t3 - 3t2 at time t,lf the…

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Q: a. Find a curve y = ƒ(x) with the following properties: i) d2y/ dx2 = 6x ii) Its graph passes…

A: given:

Q: 2.1 Can you show me the steps to solve this problem? 27) If f(x) = 3x^2 - x^3, find f'(1) and use it…

A: To determine the equation of tangent line to the given curve and the derivative of given equation at…

Q: The curve x = 1 - 3t2, y = t - 3t2. If tangent at point (1 - 3t2, t - 3t2) inclined at an angle θ to…

A: Given, x=1-3t2    ....(i)y=t-3t2    .....(ii)Now diffrentiate equation (i) and (ii) with respect to…

Q: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2. if at any point (x, y)…

A: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2.   We have to find the…

Q: 4. An arch is to be constructed so that its shape follows the curve y=-x +10x, where x measures the…

A: GIven equation of the curve is, y=-12x2+10x where x be the horizontal distance along the ground. y…

Q: 3 x5 from the point (0, 0) to the point (xo, f(xo)) is L = 243 (730)-1) If the length of the curve y…

A: TO FIND LENGTH OF THE CURVE AND COMPARE WITH THE GIVEN VALUE AND THEN FIND X0.

Q: A particle's position along the x-axis is measured by x(t) = t – 2t – 4t where t > 0. Find the…

A: Given: x(t)= t3-2t2-4t

Q: 10. (a) Find an equation for the line tangent to f(x) = x³ + 4x² at the point x = 1. (b) Find the…

A: Consider the following equation of curve: y=x3+4x2 Substitute x=1 in the above equation:…

Q: (x2 + x 2) + 3 at the point (1, 3) 18. Show that the tangent to the curve y = is also the tangent to…

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Q: 1. Trace the curve whose equation is x* – x' y = -7x² + x+6 х* + 3х-10 Identify the following a.…

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Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

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Q: Q-5. The velocity of a particle moving along a line is given by v(t) = 4t³ – 3t² at time t,lf the…

A:

Q: (a) Find an equation of the tangent to the curve y = ex that is parallel to the line x – 4y = 1.(b)…

A: A straight line passing through the point has an equation where m is the slope of the line.…

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Q: Q4/ Find equations for the horizontal tangents to the curve y = x3 – 3x – 2 also find equations for…

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Q: find the equations of the tangent lines at the point where the curve crosses itself. x  =  t3 − 7t…

A: Given data:   The given value of x is x=t3-7t. The given value of y is y=t2.   Suppose the curve…

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Q: a) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the…

A: Given       y2 = x3+3x2 DIfferentiate both the sides:→   ddx(y2) =ddx(x3+3x2)   2ydydx   =3x2+6x…

Q: The equation of a curve is y = 4x³ + px², where p is a positive constant. Find the stationary points…

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Q: y = ) «² A (x² + 2)= Q4/ Find the length of the curve y = from x= 0 to x= 3.

A: Given,y=13x2+232differentiating both the sides w.r.t. xdydx=1332x2+2122xdydx=xx2+212

Q: (a) Find the slope m of the tangent to the curve y = 5 + 4x2 - 2x³ at the point where x = a. m = (b)…

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Q: e-Sx at the point where x = 0. Find an equation of the line tangent to the graph of y = x³+1

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Q: d?y =6-9x and which passes through the points (0, -1) and (2, 3). Find the equation of the curve for…

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Q: 12 A curve has equation y = 3-2x dy (1) Find dr A point moves along this curve. As the point passes…

A: Consider the following equation of curve: y=123-2x dxdt=0.15 units per seconddydt=0.4 units per…

Q: Q-5. The velocity of a particle moving along a line is given by v(t) = 4t³ – 3t2 at 3 on the line,…

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Q: Air drop—inverse problem A plane traveling horizontally at 100 m/s over flat ground at an elevation…

A: Given: The trajectory of the packet is given by x=100ty=-4.9t2+4000t≥0

Q: 2(x2+y2)2=25(x2-y2) Find the slope of the tangent line to the curve at each of the points. Make…

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Q: The equation of a curve is x³-x²y-y³=3 a)find dy/dx in terms of x and y b)find the equation of the…

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Q: 3) An object moves along a coordinate line. Its position S (in meters) from the origin at any time t…

A: Ans: when the velocity of the object is -2m/s then the position of the object will be  -5 meters…

Q: If you will draw the graph of y=x^2 (x-1), how will the graph behave at the x-axis?   A) The graph…

A: y= x2(x-1)at x = 0:y = 0(0-1)y = 0and at x=1, y=12 (1-1)Hence, The graph crosses (0, 0) and (1, 0).

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.