If you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Area=_______

If you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Area=_______

Use Newton's method to approximate the indicated root of the following equation correct to six decimal places. The root of 2x^3−6x^2+3x+1=0in the interval [2,3].

Use Newton's Method to approximate √10 to 6 significant figures starting with x0=3.5. Compare with the value obtained from a calculator. √10≈________

Find f if f′′(x)=sin x + cos x, f′(0)=3, and f(0)=2. f(x)=_____

Find f if f′(x)=6x−[3/x^4], x>0, and f(1)=3. f(x)=_____

Find f if f′′(x)=4−6x, f(0)=3, and f(2)=−8. f(x)=_____

Use the Midpoint Rule with the value of n=4 to approximate the integral pie/2 cos^2 x dx ∫ ...

Find the absolute maximum and absolute minimum values of the function f(x)=x^3−12x^2−27x+10 over each of the indicated intervals. a) Interval [-2,0] 1. Absolute max= 2...

Find all critical values for the function f(r)=[(3r)/(6r^2+10)] and then list them (separated by commas).

Find dy/dx in terms of x and y if x^3y−x−3y−10=0. dy/dx=____

Find dy/dx in terms of x and y if 2xy+4x+y=6. dy/dx=____

Find dy/dx in terms of x and y if x^9+y^2=√2 dy/dx=_____

g(x)=∫ (x on top, 0 on bottom) √(1+6t) dt, use fundamental theorem of calculus find g1(x) (derivative of g(x). )

If ∫ (7 on top, 1 on bottom) f(z)dx= 16 and ∫ (7 on top, 6 on bottom) f(x) dx= 3.3, find ∫ (6 on top, 1 on bottom) f (x) dx

Let \displaystyle g(x)=\int_0^x {\sqrt{1+6 t}}\,dt. Use the Fundamental Theorem of Calculus to find g'(x).

The tangent line to y=f(x) at (−8,−9) passes through the point (7,7). Compute the following. a) f(-8) b) f'(-8)

Suppose that an object moves along an s-axis so that its location is given by s(t)=t^2+8t at time t. (Here s is in meters and t is in seconds. a) Find the average velocity of the object in...

The limit lim x→1 x^7−1/x−1 represents the derivative of some function f(x) at some number a. Find f and a. f(x)=_____ a=______

Let f(x)=−5x+(−5). Find the largest δ so that |f(x)−f(a)|<ϵ when |x−a|<δ. δ=________

Let f(x)=x^2−8x. To prove that limx→4f(x)=−16, we proceed as follows. Given any ϵ>0, we need to find a number δ>0 such that if 0<|x−4|<δ, then |(x2−8x)−(−16)|<ϵ. What is the (largest)...

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