Double-tap the Home button to access the app switcher -> Swipe left or right to find the application you want to close -> Swipe up over it to close it.
*You can quit up to three applications at a time by placing you fingers over them and and swiping up.
Here is a video demo of how to close apps through the app switcher:
If you are forced to restart your mobile device too often, and your problems still remains (you are still unable to close some applications), consider hard-resetting your device.
To learn how to hard-reset your device, check out the don't know how to reset my device solutions.
Press and hold the Power ON/OFF (Sleep/Wake) button until a slider appears -> Move the slider to the right to power off the device
Press and hold the Power ON/OFF (Sleep/Wake) button again after 10-15 seconds, to turn on the device.
If the above-mentioned method didn't work, press and hold the Power ON/OFF (Sleep/Wake) button and the Home button at the same time and hold them until the Apple's logo appears.
Note: No data will be lost during this process.
Maybe your device has a more serious problem for which you are not aware of. If you tried everything but nothing worked, take your device to a repair store. They will diagnose and fix the problem.
Maybe a virus prevents your programs from closing properly. The best thing you should do is to scan it for viruses.
To learn how to check if your device is infected with a virus, check out the viruses/spywares/malware solutions.
If you are not sure which antivirus software to install, check out the don't know which antivirus software to install solutions.
Maybe your mobile device is slow and prevents the application from running properly.
To learn how to improve your mobile device's speed, check out the mobile device is slow solutions.
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