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Calculus - limit of the functions
How do I solve these functions expressed in the image below?
Step by step
Solved in 2 steps with 2 images
- Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x)=cos(9x)−cos(2x)/x^2 We want to find the limit limx→0 cos(9x)−cos(2x)/x^2 Start by calculating the values of the function for the inputs listed in this table. x f(x) 0.2 0.1 0.05 0.01 0.001 0.0001 0.00001 Based on the values in this table, it appears limx→0 cos(9x)−cos(2x)/x^2=Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x)=cos(9x)-cos(5x)/x2 We want to find the limit limx→0 cos(9x)−cos(5x)/x2Start by calculating the values of the function for the inputs listed in this table. x x f(x)f(x) 0.2 0.1 0.05 0.01 0.001 0.0001 0.00001 Based on the values in this table, it appears limx→0 cos(9x)−cos(5x)/ x2
- Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x)= cos(9x)−cos(10x)/x2 We want to find the limit limx→0 cos(9x)−cos(10x)/x2Start by calculating the values of the function for the inputs listed in this table. x x f(x)f(x) 0.2 0.1 0.05 0.01 0.001 0.0001 0.00001 Based on the values in this table, it appears limx→0 cos(9x)−cos(10x)/x2=?15.2.65 #22 Use the method of your choice to evaluate the following limit. lim y ln y/x = (x,y)→(4,0)Guess the value of the limit (if it exists) by evaluating the function at the given numbers. Report answers accurate to six decimal places. cos(3x) cos(8x) Let f(x) = - x² We want to find the limit lim x->0 cos(3x) - cos(8x) x² Start by calculating the values of the function for the inputs listed in this table. f(x) 0.2 0.1 X 0.05 0.01 0.001 0.0001 0.00001 Based on the values in this table, it appears lim x-0 cos(3x) cos(8x) x²
- Calculate the limit algebraically. (If an answer does not exist, enter DNE.) lim h→0 8h2 + h 3h2 + 3h - ________________ If the limit does not exist, say why. (If the limit does exist, so state.) -The limit does not exist because one side diverges to ∞ and the other side diverges to −∞. -The limit does not exist because only one of the left or right limits exists as a finite value. -The limit does not exist because the left and right limits exist but are not the same finite value. -The limit does not exist because it diverges to ∞ or −∞. -The limit does exist and is a finite number.Find the limit. (Hint: Let x = 1/t and find the limit as t → 0+.) lim x→∞ 2x tan(1/x)Evaluate the limit using L'Hospital's RUle if necessary. The limit of ((e^x) -1) / (sin(5x)) as x approaches zero
- Find Limit: lim t-->0 [e^(-3t)i +((t^2)/(sin^2(t)))j+cos(2t)k]; I know this has to be done component wise, I forgot how to take the limit of the j and k component => ((t^2)/(sin^2(t))) and cos(2t) from previous courses and would like an explanation on how to approach it.IN THE FOLLOWING PROBLEMS YOU WILL FIND THE LOMIT OF A FUNCTION NUMERICALLY. FIND THE VALUE OF THE LIMIT FROM THE TABLE OF FUNCTIONAL VALUES IN THE TABLE. IF THE LIMIT DOES NOT EXIST. STATE THIS. a) y=cosX-1 : X X -1 -0.5 -0.1 -0.01 0 0.01 0.1 0.5 cos X-1:X 0.04597 0.2448 0.0500 0.0040 UND -0.0050 -0.0500 0.2447 ---- lim cos x-1 : x -------- x--> 0 ---- lim cos x-1 : x x--> 0 ---- lim cos x-1 : x x--> 0Using the appropriate approached covered in Unit 6 of this course along with knowledge gained in Unit 1 and 2, verify whether the limit to infinity of n (n +1) (n + 2)-1 (n+3) -1 is equal to one.