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- Find the slope of the tangent to the graph of the following function at the point (e^2,4). Give your answer as an exact value, not a decimal approximation. y=(ln(x))^(ln(x))A. In desmos make a graph of the implicit curve, the window should be [-2,4] for x and [-4,2] for y B. Determine the derivative dy/dx C. At the point (1,-1) compute the value of dy/dx2. Find the vertical and horizontal asymptotes for ?(?) =3?−2√4?2+5. 3/ Find the derivative ?′(?) implicitly.???2? + ???2? = cos (2? + 2?)
- 6) If y = f(x) has slope −4 at x = 3, and y value 5 at x = 3, a) write the formula for the tangent line to f(x) at x=3: b) estimate f(3.02) from the tangent line: c) If f is known to be concave up (S), is f(3.02) bigger than or smaller than your answer in b)?From the graph attached answers the below questions A) What was the average velocity of the car from t = 0 to t = 50 seconds?B. What was the average velocity of the car from t = 10 to t = 50 seconds?C)Give a rough estimate of how fast was the car was traveling at1(a) t = 0 seconds(b) t = 15 seconds(c) t = 30 seconds(d) t = 50 secondsD) What does the horizontal part of the graph between t = 20 and t = 35seconds mean?E)What does the downward slope between t = 35 and t = 40 seconds mean?Each of question gives the first derivative of a continuous functiony = ƒ(x). Find y'' and then use Steps 2–4 of the graphing procedure to sketch the general shape of the graph of ƒ. y' = cot θ/2, 0 < θ < 2p
- The tangent line to g(x)at x=3 is L(x)=7x−26 (see the diagram below). Find h′(3)where h(x)=(g(x))^4. (Note: h(x)is NOT pictured below.)4. Differentiate the following function. y=5e x−5x dy/dx=nothing Enter your answer in the answer box.4.2: 3) Use linear approximation, i.e. the tangent line, to approximate 1/1.001as follows: Let f(x)=1/x and find the equation of the tangent line to f(x) at a "nice" point near 1.001. Then use this to approximate 1/1.001.
- A car is moving along a straight road in a positive direction from A to B, starting from A at a time t=0. The graph below shows the car’s velocity. How far away from A is the car at time t=6?The fungus Fusarium exosporium infects a field of flax plants through the roots and causes the plants to wilt. Eventually,the entire field is infected. The percentage f (t) of infected plants as a function of time t (in days) since planting is shownin Figure 16.(a) What are the units of the rate of change of f (t) with respect to t? What does this rate measure?(b) Use the graph to rank (from smallest to largest) the average infection rates over the intervals [0, 12], [20, 32], and[40, 52]. (d) Draw the tangent line at t = 40 and estimate its slope.Two ships are sailing in the fog and being tracked on a small screen. At some point in time, t=0, the first ship, the Andy Daria (AD), is at a point 900 mm from the bottom left corner of the screen along the lower edge. The other ship, the Helinski (H), is located at a point 100 mm above the lower left corner along the left edge. One minute later, the AD has moved to a location that is 3 mm west and 2 mm north of the previous location. The H has moved 4 mm east and 1 mm north. Assume that they will continue to move at a constant speed on their respective linear courses. Create an illustration of the situation. Create a parameterization for each of the vessels. Will the two ships collide if they maintain their speeds and directions? If so, when and where? Determine the minimum distance between the ships and the time at which they are the closest.