Find the slope of a line tangent to the curve of the given equation at the given point. y=(x^3)/4; (6,54)

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

Q: Find the difference quotient en-7 for each of the given functions. B. f(x) = 3x + 2 Find the slope…

A: Solution

Q: Differentiate y = 2(2x - 1)5/4.(2x + 1)3/4

A:

Q: Differentiate y = 3e2x/(1 + x2.)

A: y=3e2x1+x2

Q: -4 (3x² + 5x) 52

A: Using derivatives property we  can find derivatives of y

Q: Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent…

A:

Q: y = In( sech2x)

A: The objective of the question is to find the derivative of the function y = ln(sech^2(x)).

Q: By using equation qx= 2mx/(2+mx) , derive a similar equation for the more general case of an age…

A: Given: qx=2mx2+mx To Show: qxn=2×n×mxn2+n×mxn

Q: 192) Find la(21)=?

A: Note the logarithm property : logaxy=logax+logay where x,y>0 and a>0 ,a≠0 . logaan=n ; where…

Q: Derive all the possible equations of x. Given : (x-2)^2+lnx=0

A:

Q: | sech²xtanh²x dx

A: We can find the integration as below

Q: WXYZ is an isosceles trapezoid with bases WZ and XY and midsegment MN. Use the given information to…

A: Given  WXYZ is a isosceles trapezoid with  MN= 2x+1 XY=8 WZ=3x-3

Q: Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent…

A: