A ball is thrown into the air with an upward velocity of 12 ft/sec. The equation for the ball's height (h) at any time (t) is h(t) = -4t²+ 12t + 5.

Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

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Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

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Q: Find the equation of the line tangent to the curve y = 3x?(x² – 6x) at x = 2.

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Q: Find the slope of the line tangent to the graph of x^2+2xy^2+3y=31 at the point(2,-3)

A: The slope of the tangent line can be calculated by using the derivative of the function at the point…

Q: find the slope of the line tangent to the curve x2=y2+3/2xy at (4,2)

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Q: Find an equation of the line tangent to the curve defined by x2 + 6xy + y 32 at the point (2, 2).…

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Q: dx J x* – 1

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Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

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Q: Find the slope of the line tangent to the curve 5x3 + 2x5y − y2 = 2 at the point (1,3) Write your…

A: Explantion: Given that: 5x3+2x5y-y2=2 Concept: slope of line m=dydx dxndx=nxn-1 duvdx=udvdx+vdudx

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A: Curve y=ax3+bx2+cx+d is tangent to the line y=3x+8 at the point (-2,3). The curve y=ax3+bx2+cx+d has…

Q: ƒ (x, y) = ln (√√x²y³) f

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Q: (b) Find the equation of the tangent line to the curve 8x²y3 – 5x? + 7y³ = 10(x – 3y), at the point…

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Q: When we are standing at the point (1,-3), the function f(x, y) = 3x²y+xy is increasing most rapidly…

A: We have to find the direction of  rapid increase of the function using gradient of the function.

Q: Find an equation for the line tangent to the graph of  f(x)= 2xex at the point (3,f(3)). y=?

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Q: Find the equation of the line tangent to the curve 3t2 + 8,y = 8t + 3 at t = 2

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Q: Find an equation of the line tangent to the curve y = x²e*-3 at x = 3.

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Q: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

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Q: d'y If x =t-sint , and y=1-cost, find

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Q: 2.) What is the equation of the line tangent to y(x) x- 2r3+6x-3 at r =-1?

A: Follow the steps .

Q: Find the equation of the line tangent to 3x²y + 4xy2 = 6x² + 5y at the point (1,).

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Q: , хуян ху exy ху en y e xy enx = x=c e x = C/ - -

A: Yes, its correct.

Q: Find the equation of the line tangent to y = x2 - 1 going through x = 1

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Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A: To find the distance between objects when they have same velocity.

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

Q: 4. Find the equation for the line tangent to a. y= x²- 3 x + 5 at the point (2, 3)

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Q: If f(x)=7+6x−5x^2, find the equation of the line tangent to the curve f(x) at x=4 y = ?

A: We have to find tangent line equation. Given f(x)=7+6x−5x2 and at x=4 we have to find tangent line…

Q: Find the equation of the line tangent to the curve x = 3t2 + 8 , y = 8t + 3 at t = 2

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Q: Find the point in the parabola y2 = 4x at which the rate of change of the ordinate and abscissa are…

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Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

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Q: The line y=3x+6 is tangent to the graph of y = (-48)/(x-6) at the point ?

A: The given equation of tangent is y=3x+6 and its tangent to graph of y=-48x-6. To find the points at…

Q: For the curve y = ax³ + bx² + 12x - 7, what values of a and b will make the tangents to the curve at…

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Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

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Q: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

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Q: Use the method of variation of parameters to solve. y" + 4y = 8 tan t - "/2<t<"/2

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Q: ) Find an equation of the line tangent to the curve y = x²e²-3 at a = 3.

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Q: Q1: solve: * y" – 2y' + 2y = 1+ et – sint + te cost

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Q: What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=O?

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Q: Find and in terms of t. dx2 x= -9 sint, y = cost dx dx2

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Q: In the open interval (0, T1/2) , find the point where the slope of the curve is 4? y = 3x* – 8x +…

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Q: 2. (2x + y – 4)dx + (x – 3y + 12)dy = 0 -

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Q: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

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Q: Solve t-r sec'y= 2g tan y,

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Q: y = e² -Vx sec 6x 3

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Q: What is the equation of the line that crosses the y-axis at 2 and h. a unit rate of ?

A: We have to find the equation of the required line. The required line crosses the y axis at 2, that…

Q: Solve the IVP d'y = 4sec 2x tan 2x, y' (0) = 4, y(0) =-1 dx2

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Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2

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Q: Find the equation of the line tangent to the curve f(x) = 4x² - 6x +39 at x = 1.

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Q: The equation of the line that is tangent to the curve y=2x3−6x and is perpendicular to 18y+x+3=0…

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Q: At what point on the parabola y=3x^2+2x is the tangent line parallel to the line y=10x-2? Use first…

A: We have to find the point.