Calculus Answers

Trace the curve y² (a²+x²)=x²(a²-x²), a>0

A triangle has a base 12 ft long and an altitude 8 ft high. Find the area of the largest rectangle that can be inscribed in the triangle so that the base of the rectangle falls in the base of the triangle.

If three sides of trapezoid are each 6 inches long, how long must the fourth side be if the area is a maximum.

If the length of the hypotenuse of a right triangle is 10, find the length of the other sides when the area is maximum.

A closed box, whose length in twice its width, is to have a surface area of 192 square inches. Find the dimensions of the box when the volume is maximum?

1.g(x)=2^5x 4^3x^2

2.Given 𝑒 𝑥 𝑠𝑖𝑛𝑦 + 𝑒 𝑦 𝑐𝑜𝑠𝑥 = 1 , find 𝑦′ .

3.y=e^x^3 3^e^x

g(t)=3t/e^6t

f(x)= e^x sine^x

1.g(t)=3t/e^6t

2.y=e^x^3 3^e^x

3.f(x)= e^x sine^x

4.g(x)=2^5x 4^3x^2

5.Given 𝑒 𝑥 𝑠𝑖𝑛𝑦 + 𝑒 𝑦 𝑐𝑜𝑠𝑥 = 1 , find 𝑦′ .

lim= (X⁵ + 3X² + 3) / (99X² + 44X + 13)

(x→∞)

𝑓(𝑥) = 7 ^𝑒 𝑥𝑐𝑜𝑠x