Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
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Identical expressions
- one +(one + seven *x/ two)^x
- 1 plus (1 plus 7 multiply by x divide by 2) to the power of x
- one plus (one plus seven multiply by x divide by two) to the power of x
- 1+(1+7*x/2)x
- 1+1+7*x/2x
- 1+(1+7x/2)^x
- 1+(1+7x/2)x
- 1+1+7x/2x
- 1+1+7x/2^x
- 1+(1+7*x divide by 2)^x
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Similar expressions
- 1+(1-7*x/2)^x
- 1-(1+7*x/2)^x
Limit of the function 1+(1+7*x/2)^x
The solution
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[src]
/ x\
| / 7*x\ |
lim |1 + |1 + ---| |
x->oo\ \ 2 / /
$$\lim_{x \to \infty}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right)$$
Limit(1 + (1 + (7*x)/2)^x, x, oo, dir='-')
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = \infty$$
$$\lim_{x \to 0^-}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = \frac{11}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = \frac{11}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = 2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = 2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = \frac{11}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = \frac{11}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\frac{7 x}{2} + 1\right)^{x} + 1\right) = \infty$$
More at x→-oo
The graph