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## Questions

### Subject:Number Theory

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Question:

Calculate- $$112 * 5^4$$

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Ans- 70000 Solution- $$112*(\frac{10}{2})^4 = \frac{112*10^4}{2^4} = \frac{1120000}{16} = 70000$$

### Subject:Calculus

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Question:

Find the limit of $$\frac{cos(x)-cos(2x)}{1-cos(x)}$$ as $$x\to0$$.

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$$\lim_{x\to0} \frac{cos(x)-cos(2x)}{1-cos(x)} = \frac{0}{0}$$ $$\therefore$$, this limit does not exist. But, on applying L'Hospital's Rule, i.e., $$\lim_{x\to c} \frac{f(x)}{g(x)} = \lim_{x\to c}\frac{f'(x)}{g'(x)}$$ (if the latter limit exists) Hence, $$\lim_{x\to0} \frac{cos(x)-cos(2x)}{1-cos(x)} = \frac{-sin(x)+2sin(2x)}{sin(x)} = \frac{-cos(x)+ 4cos(2x)}{cos(x)} = \frac{-1+4}{1} = 3$$

### Subject:Photoshop

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Question:

What are some applications of Adobe Photoshop?

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Photoshop with it's wide range of tools and versatility, can be used in any field you can think of to enhance, modify or create complex images. Some of the most common uses are- 1. Poster, logo designing, art work - Photoshop has features that give you the freedom to bring imagination to life. 2. Animation - Photoshop enables you to create complex models and objects and animations. 3. Web designing - create background, buttons, and other elements you can use on a web page. 4. Image restoration - can be used by archaeologists or in forensics or in medical field to enhance images for analysis. The list is virtually endless!

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