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- Evaluate the limit based on the limit theorems. Give your step by step solution. 1. lim 3x(x+5)= x➪41) Find the indicated limit if it exists. a) limx→0 squareroot x+4-2/x b) limx→−1.5 8x3+27/2x+31a. Find the limit. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.) lim t-> -∞ ( (6t^2+t)/(t^3-7t+1)) 1b. Find the limit. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.) lim u-> -∞ ((u^2+1)(8u^2-1)) /(u^2+9)^2 1c.Find the limit. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.) lim x-> ∞ sqrt(x+6x^2)/(8x-1)
- 1. Broadly speaking, what are the Limit Laws, and why do they help us calculate limits?2. In Example 3, there is a step where the function x2 − 1x − 1is changed to x+ 1. But unlike the secondfunction, the first function is undefined at x = 1. How can we justify changing functions this way?3. Explain the flaw in the following calculation:limx→0x2sin(1/x) = (limx→0x2) · (limx→0sin(1/x)) = 0 · (limx→0sin(1/x)) = 0.15.2.25#11 Evaluate the limit. lim 8y^2-512/xy+8x (x,y)--->(8,-8) Find an expression that is equal to f(x,y)=8y^2−512/xy+8x, for all (x,y) in the domain of f, that will be better suited to find the limit, if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.How do I find a limit in terms of constant a? lim ((2/a+h)-(2/a)) / h h->0