Simple calc problem?

Question

I have a graphing calculator but I can't figure this out using algerbra.

lim ((-7/5) + ((7)/(x+5)) / (x)
x --> 0

Answer 1

This one requires quite a bit of algebra to solve. First, re-write the expression so that (-7/5) and (7/(x+5)) have a common denominator:

(-7)(x+5) / [(5)(x+5)] + (7)(5) / [(5)(x+5)]

= (-7x - 35) +35 / [(5)(x+5)]

= -7x / [(5)(x+5)]

Now, that was the top part of the large expression. When you put that back into your original problem, the x's will cancel, and you can take the limit directly.

Answer 2

volume = length x Breadth x properly. subsequently it has a sq. base so length = Breadth. also all of us keep in mind that volume = 32 000cm^3 So we've the equation (a million): 32000 = L^2 x H the quantity of fabric used is the exterior component of the field, subsequently you've: the bottom section = length x Breadth = length^2 (As length = Breadth as suggested previously) the realm of the perimeters = length x properly x 4 (as there are 4 sides) So the finished component of fabric, A is: A = length^2 + 4 x length x properly. So we've Equation (2): A = L^2 + 4 x L x H If we reorganise (a million) to locate H in words of L: 32000 = L^2 x H H = 32000/L^2 we've equation (3): H = 32000/L^2 If we replace (3) into (2): A = L^2 + 4 x L x (32000/L^2) Now simplify it: A = L^2 + 4 x L x (32000/L^2) A = L^2 + (128000 x L)/L^2 A = L^2 + 128000/L this can provide us equation (4): A = L^2 + 128000/L we want to locate at the same time as A is a minimum. this suggests it must be a turning element on the graph. for this reason the gradient must be 0. Differentiate: A = L^2 + 128000/L dA/dL = 2 x L + -a million x 128000/L^2 dA/dL = 2 x L - 128000/L^2 it is equation (5) dA/dL = 2 x L - 128000/L^2 For turning factors dA/dL = 0, for this reason: 0 = 2 x L - 128000/L^2 128000/L^2 = 2 x L 128000 = 2 x L x L^2 128000 = 2 x L^3 64000 = L^3 L = 40 there is purely one real root; L = 40 we ought to continually truly examine to make certain that it is a minimum turning element: If we enter L = 39 into equation (5): dA/dL = 2 x L - 128000/L^2 dA/dL = 2 x 39 - 128000/39^2 dA/dL = a -ve answer. If we then enter L = 40-one into equation (5): dA/dL = 2 x L - 128000/L^2 dA/dL = 2 x 40-one - 128000/40-one^2 dA/dL = a +ve answer. So from this we may be able to work out that the gradient of the curse because it techniques element L = 40 is adverse, then that is 0, then that is advantageous at the same time as L > 40. The graph has the shape _/ and is subsequently L = 40 is a minima, precisely what we were desirous to locate. Now that we are advantageous that L = 40cm is the splendid L value it is only a case os substituting lower back into previously equations to locate the different dimensions. we may be able to locate H utilising equation (3): H = 32000/L^2 H = 32000/(40^2) H = 32000/1600 H = 20 So now we would were given L = 40, H = 20 and Breadth = L = 40 shall we examine to make certain that the quantity is nice: V = L^2 x H V = 40^2 x 20 V = 1600 x 20 V = 32000 So, the answer's length of the perimeters of the sq. base are 40cm and the properly of the field is 20cm. i wish you may follow the operating.

Answer 3

I think it's -7/5 because when anything is divided by 0 it is undefined and becomes 0 and you are left with whatever's left in the equation which is -7/5.

Answer 4

the answer is 4

Answer 5

the answer that i got was 3