Find and plot the cubic spline S satisfying S(0) = 1, S(1) = 3, S(2) = 3, S(3) = 4, S(4) = 2 and with S' (0) = 0 and S'(4) = 1.

Q: the line (x/a)+(y/b)=1 moves in such a way that (1/a\power{2})+(1/b\power{2})=(1/c\power{2}) ,where…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

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Q: Suppose the slope of the tangent lir

A: Given that the slope of the tangent line at any point on a curve is…

Q: with y(0) -1

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Q: Find the formula for a parabola with its vertex at (9,4) and with a second derivative of -3. f(x)=

A: let's equation of parabola is given by y=ax2+bx+c                                              ..1…

Q: f(x)=8x³ +7x-5-

A: The given function fx=8x3+7x-5. We have to show that the curve does not have a slope tangent 5.

Q: Find the derivative of the following function. y = In(6x² – 7x) – 4x А) 18х? -7х x(6х* - 7) В) 1 - 4…

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Q: The equation of the tangent line to the curke x? + y = 36, at (6,-16) is %3D y = (x+6) + 16 16 16 16…

A: we have to find the equation of the tangent line to the given curve at (6, -16)

Q: Find G′(w) if G(w)=5/ 9w^5 +7 sqaure root w. G'(w)

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Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: Find f. f ''(t) = 9/ squareroot t,    f(4) = 31,    f '(4) = 12

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Q: (8 points) Find the slope of the line tangent to the graph of 1 f (x) = 2x* – 32x + 17x2 – 9x + 4 at…

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Q: If the time 26 + 1%/16 = 1 a that moves in such a way b 1/2 + 1/2 = 1/², where c is a constant, they…

A: Variable line is                xa+yb=1                 ......(1)Any line perpendicular to (i) and…

Q: 8) Suppose you are at the point (2, 1, 82) on the hill given by f(x,y) = 100-4x²-2y (where the z…

A: The objective of this question is to understand the concept of directional derivatives and gradient…

Q: 3) Find all points (x, y) on the graph of x2/3+y²/3 = 8 where the tangent lines have slope –1.

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Q: 10. State whether each equation is true or false.(a) (p+q)^2=p^2+q^2 (b) sqrt( ab)= sqrt a* sqrt b…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find y as a function of if y(0) = 19, y'(0) = 19, y"(0) = 4, y"(0) = 0. y(x) = y(4) 4y" + 4y = 0,

A: y(4)−4y′′′+4y′′=0y(0)=19,y′(0)=19,y′′(0)=4,y′′′(0)=0

Q: find dy/dx if y=((t-1)/(t+1))^2 and x= (1/t^2)-1 at t=2

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Q: For each of the following sequences, if the divergence test applies, either state that lim an does…

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Q: The region bounded by f(x) 2x² + 12x + 14, x = = 0 is rotated about the y-axis. Find the volume of…

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