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If x4+y4=16, use the following steps yo find y''.
a. Use implicit differentiation to find y'.
b. Use the Quotient Rule to differentiate the expression for y' from part (a). Express your answer in terms of x and y only.
Find y'. Simplify all answers.
a. x²y + xy² - y³ + x² = 2
b. sqrt(2xy) + y²-xy²=1
c. sinx + cosy = sinxcosy
d. y = x^x^x
e. y = (sinx)^2x
f. ln(x²+y²) + 2arctan(y/x) = 1
g. (x+y)³ = (x-y)²
a. The raduis of a sphere was measured and foubd to be 20cm with a possible error in the meadurement of at most 0.05cm. What is the maximum percentage error using this value of the radius to compute the volume of the sphere? The formula is V=4/3(πr³) where V us the volume and r is the radius if the sphere.
b. Find the slope of the line tangent to the graph of the function y=x²+3x+4 at x=0.
c. Find the slope if the line tangent to the function f(x)=sqrt(4-5x) at x=-1.
d. Find the slope of ths line tangent to the graph of the function f(x)=x+2/2x+5 at x=-2.
Given the function y=√x
a. Find the differential dy.
b. Evaluate dy and ∆y if x=1 and dx=∆x=1
c. Find the equation of the tangent line at x=1
d. Sketcg the graph of the curve y=√x and the tangent line in the Cartesian Plane using a scale of 1 unit = 1cm. Show in your diagran the line segments dx, dy, and ∆y. (Note: the curve us an upper semi-parabola whose vertex is at the origun and concaving to the right. Use 0, 1, 4, and 9 as x-coordinates.)
Determine for which value of "\\alpha" the given series converge absolutely, converge conditionally, or diverges.
- "\\displaystyle\\sum_{k=1}^ \u221e ((-1)^k*\n\\alpha" ^(k)k)/2
- "\\displaystyle\\sum_{k=1}^ \u221e ((-1)^k*\n\\alpha" k)/k
Can you kindly explain a little bit so that I can try to solve other problems. Thank you so much.
3.Using the definition of "Big-O" determine if each of the following functions, f(x)=(xlogx)^2−4 and g(x)=5x^5 are O(x^4) and prove your claims.
The power from an engine (in W) is represented by Power, where t is the time in seconds.
- Draw a graph of power against time
- Show the area on the graph which represents the energy converted between 5 and 10 seconds
- Evaluate (using the rules of integration) the energy between 5 and 10 seconds
Part of the machine moves with a velocity given by the expression mm/s
- Calculate the displacement over the first 5 seconds of motion.
Consider a moving body B whose position at time t is given by R(t)=t2 i+t3 j+3 tk .
[Then V (t) = dR(t) / dt and A(t) = dV (t)/dt denote, respectively, the velocity and acceleration of B.]
When t = 1, find for the body B:
(a) position (b) velocity v (c) speed s (d) acceleration a
Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total area of the pen
Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum.
