12:35 ll 86% Assignment 1 Cal - Read-only ビy Read Only - You can't save changes to this fi... Show sufficient work to demonstrate understanding. Provide clear work and answers; your an- swers need not be simplified however. Each numbered or lettered response is equally weighted. 1. Find f'(t) if f(t) = dy if y = dx = VIn x 2. Find 3. Find (2tant) dy if y = sec dx (4) 4. Find 5. Find y if y = log(cot x) dy 6. Find if y = tan dt 1 of 3 II 12:35 l 86% Assignment 1 Cal - Read-only ビy Read Only - You can't save changes to this fi... 11. A large spherical snowball is melting. Its volume is decreasing at a rate of 100 cm³ /hr. How fast is the radius of the snowball decreasing when the radius is 25 cm? Note: Be sure to include the appropriate units in your response. Recall that the volume, V, of a sphere of radius r is given by V = ar. x² + 1 12. Let f(x) Show sufficient work in determining ... (a) the intervals over which f is increasing, the intervals over which f is decreasing, and any local extrema. Be sure to indicate whether an extremum is a maximum or a minimum. (b) the intervals over which the graph of f is concave up, those over which it is concave down, and any inflection points. 13. Find the absolute maximum obtained by s(t) = 2t3 – 3t² – 36t +5 on the interval [0,4]. You must show sufficient work for credit here. II

Q: F(t) = e^2t - 8/ 1-t Will this be undefined? And why? And which values of t is the function

A: given F(t) = e^2t - 8/ 1-t

Q: Differentiate the function f(t) = t^3 − it^2 when t = 2

A: Here, f(t)=t3-it2⇒f'(t)=3t2-i(2t)⇒f'(t)=3t2-2ti

Q: Consider f(t)=. Find f'(1).

A: Given ft=<6t2,5t3,8t4> Differentiating the given function with respect to t, we get…

Q: Let f(x)=(2^x-2^-x)/2 and g(x)=(2^x+2^-x)/2.  Compute f^2-g^2.

A: in this question f(x) and g(x) is given f(x)=2x-2-x2 g(x)=2x+2-x2 we have to find f(x)2-g(x)2

Q: ind the exact location of all the relative and absolute extrema of the given function: h(t)= 2t^3…

A: find critical point and check sign of double derivative at critical point

Q: f(t)=4t^2-3  Find the Left endpoint  Right endpoint

A:

Q: Let p(x)=−x^3+1/3⋅x^2+1. Calculate:  p(1/2)

A: The function given is p(x)=-x3+13x2+1. We are asked to find the value of this function when x=12.

Q: limit as t-0 ((e^-2t)-1)/t,t^7/(t^8-t^7),-8/(2+t)

A:

Q: Let f(x)=-2x/x-1, find f^-1(x)

A:

Q: Let f() - 4x2- 19x, Determine the largest n for whichfe C.

A: Given fx=4x223-19x7111.  f∈Cn implies that nth derivative fn exists and continuous. Consider…

Q: f(x)=sqrt(x+1) find f(t^2-1)

A: We have to find the function

Q: Let f(x)=x^3−x.Find where f(x)<0.

A:

Q: Find two positive numbers so that the sum of the first and twice the second is 100 and the product…

A: Let two positive numbers are x and y. Given that the sum of the first and twice the second is 100 .…

Q: f(x) = 4x^2-12x+7   how is this function concave wherever it is defined?

A: Given:

Q: Letf(x) =x^x^xforx >0.Findf′(x).

A:

Exponential Growth Model

The relation that represents an exponential function is: