(ii) Sketch the graph 'V' vs. 't'for 0 st< 5t. 2. Velocity 'v' of a vehicle during the application of brakes according to time 't'is given by v = 10e -kt where 'k'is a friction constant. (i) Determine the friction constant 'k' at t = 30s and the velocity is reduced to 2.5ms-1. (ii) Find the velocity 'v'at t = 45s.

Q: 8. Estimate the slope of the tangent line to the curve y = -2x at x=-4, and then use it to find the…

A: Given curve is y=-2x3 To find the slope of tangent at x=-4. Solution: Differentiating the given…

Q: y=8sin(x)cos(x) ; x=pi/3

A:

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: We have  y=ax2+bx+c        at (2,28)           and               y=4x

Q: The graph of f(x) = −sin x has infinitely many tangent lines that pass through the origin. Use…

A:

Q: The slope of tangent lines to a curve y=f(x) is given by f'(x)=1/√√x +4x^3-1. If the point (1,6) is…

A: Equation of curve

Q: Find the equation of the line tangent to the graph of f(x) = – = -3 cos (x) at x = 3 m(x – xo). You…

A: given: the function f(x)=-3cos(x) the point is x=-π3

Q: Find the equation of a curve passing thorugh the point (0,2) and having slope x +ex-sinhx at any…

A:

Q: coat of paint of thickness 0.07 cm is to be applied uniformly to the faces of a cube of edge 40 cm.

A:

Q: A coat of paint of thickness 0.03 cm is to be applied uniformly to the faces of a cube of edge 29…

A: Let the side length of the cube be S = 29.Side increase on each side = 0.03 cm.Total increase in…

Q: Find the equation of the tangent plane to the graph of 5y f(x, y) = at the point (9, –1). (Use…

A: The equation of the tangent plane at point (x1, y1, z1) is z-z1=∂z∂x(x1, y1, z1)(x-x1)+∂z∂y(x1, y1,…

Q: 2. Use implicit differentiation to find tangent at the given point: (a) xy + y² = 3-3x² at (-1,1).…

A: use implicit differentiation, I try to provide typed solution, if it is helpful like it.

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A:

Q: The width and length of a rectangle are measured to be 3 m and 5 m, respectively. These come with an…

A:

Q: The graph at the right show a relative minimum at the point , but y' # 0. How could we use the…

A: The cusp points on the curve can be identified as follows: If the function f(x) has the first…

Q: Find an equation of the tangent line to y sin 2x = x cos 2y at the point π/2 , π/4 . Do not…

A: First we will find Differentiation of given equation to get slope of the tangent line. Now equation…

Q: Assume that it costs a company approximately C(x) = 529,000 + 160x + 0.001x2 dollars to manufacture…

A:

Q: 4) Find the slope of the tangent line to the curve 4 y = 3(х3 — 2х2 + 3х — 5) at the point (2,) Give…

A:

Q: Find the equation of the tangent plane to the graph of 9y f(x, y) = at the point (4, –-1). (Use…

A: The Equation of the tangent plane: - z0=(x0,y0) is a point in the domain of f, and defined by a…

Q: The tangent lines to the graph of f(x) =x² grow steeper as x in- creases. At what rate do the slopes…

A: Given function is, f(x)=x2

Q: The slope of the tangent line to the graph of f(r) at the point (-7,5) is The equation of the…

A: Topic - equation and slope of tangent line to curve

Q: 1. A sag equal tangent vertical curve is designed for 45mi/h. The low point is 237ft from the PVC at…

A:

Q: | 25. a. Find a curve with a positive derivative through the point (1, 1) whose length integral…

A: a) Find the curve-

Q: What is the equation of the tangent line to the function y = e-* - arcsin) x+1 2. at x= 0 ? A) y-…

A:

Q: The pressure difference of the two ends of a small pipe of cross-sectional radius x is given by P =…

A: Here in this question we have to find change in pressure across pipe given change in radius.

Q: Suppose you are climbing a hill whose shape is given by the equationz= 1000−0.01x2−0.02y2, where x,…

A:

Q: The slope of the tangent line to a curve at any point is (5x² - y) ex+y If the curve passes thru…

A:

Q: One side of a right triangle is 150 m long and its adjacent angle is t/3 radians, with t/60 radians…

A: Use derivative

Q: The slope of the tangent line to the curve y 4 at the point (4, 1) is: - The equation of this…

A: The slope of tangent to any curve is determined by the derivative . So, slope of the tangent…

Q: 4 at the point ( 6, The slope of the tangent line to the curve y is: 3 |

A: The  Slope of the tangent line is = -(1/9)

Q: 8. Find the slope of the tangent of the curve x² + y² = 10 at the point (1, -3).

A:

Q: It can be shown that the Difference Quotient (D.Q.) of f (x) = sinx is h-[sinx(cos(h) – 1) +…

A: We are provided that the Differential Quotient (D. Q.) of f(x)=sinx is h-1sinxcosh-1+cosx sinh, if…

Q: What is the value of the slope of the tangent line to the curve *y+y²=5 passing through the point…

A:

Q: derivative of g(x)= intergral from 1 to root x, (z^2)/z^4+1

A: ddx∫1xz2z4+1dz

Q: Suppose y = f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A:

Q: The slope of the tangent to y = 2 – x2 at the point (1,1) is

A:

Q: 2. The radius and height of a right-circular cylinder are measured with errors at most 0.1 inches.…

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Q: Find the equation of the tangent and the nirmal to the curve y=5x4 at the point (1,5)

A: Given curve,  y = 5x4  To find the equation of tangent and normal at the point (1, 5)

Q: 1. Find the slope of the graph of the function f (x) = v3x + 4 at x = 7. Then find an equation of…

A: equation of tangent line is (y-y1) = slope (x-x1)

Q: 4 at the point ( 3, The slope of the tangent line to the curve y is:

A:

Q: 16. Determine the horizontal tangents on the curve y = 2x'-18x.

A:

Q: 2. One side of a right triangle is known to be 150 cm long and the adjacent angle is measured as…

A: The given problem is to find the maximum possible error in area of triangle when one side and angle…

Q: 1. Explain why there are no tangents to the curve y = with negative slope. (Explain by 2x+1 4x+3…

A: Given: y=2x+14x+3 To explain: Why there is no tangents to the given curve.

Q: How did he get the second derivative step by step and a clear line please 3 F(x) = 1+e siny x Fex)…

A: Let fx=1+e-xsin 4x

Q: What is the value of the slope of the tangent line to the curve x²+ 4.xy +y² =13 passing through the…

A: topic - slope of a tangent at a point on a curve

Q: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x-coordinate…

A: It is given that the x coordinate increases at a steady 10 m/sec. dxdt=10msec. The equation of…

Q: The derivative of y = In(sin(ex + 1)) is O y' = -ex cot(ex + 1) the above y' = -ex tan(ex + 1)

A:

Q: ind an equation of the tangent line to the curve at the point (3, 4).  y=(x-1/x-2)+2

A:

Q: #8.) Determine the slope of the tangent at point (1,4) on the graph of f(x) = (9-x²) ²/

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

Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

A: