Hitunglah nilai minimum dan maksimum dari fungsi berikut ini : 0\;\mathrm{dan}\;0^\textdegree\leq x\leq360^\circ" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»w«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»d«/mi»«/mrow»«mrow»«msqrt»«mn»3«/mn»«/msqrt»«mo»§#160;«/mo»«mi»sin«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mi»x«/mi»«/mrow»«/mfrac»«mo»,«/mo»«mo»§#160;«/mo»«mi»d«/mi»«mo»§#62;«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»dan«/mi»«mo»§#160;«/mo»«msup»«mn»0«/mn»«mo»§#176;«/mo»«/msup»«mo»§#8804;«/mo»«mi»x«/mi»«mo»§#8804;«/mo»«mn»360«/mn»«mo»§#176;«/mo»«/math»" role="math" src="data:image/png;base64,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" style="max-width: none;">

Pembahasan

Ingat konsep : a cos x + b sin x R ​ = = ​ R cos ( x − α ) , dengan a 2 + b 2 ​ dan α = tan − 1 ( a b ​ ) ​ Limit kanan dan limit kiri : x → a − lim ​ f ( x ) = x → a lim ​ f ( x ) = x → a + lim ​ f ( x ) = L Dari soal diketahui : 0\;\mathrm{dan}\;0^\textdegree\leq x\leq360^\circ" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»w«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»d«/mi»«/mrow»«mrow»«msqrt»«mn»3«/mn»«/msqrt»«mo»§#160;«/mo»«mi»sin«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mi»x«/mi»«/mrow»«/mfrac»«mo»,«/mo»«mo»§#160;«/mo»«mi»d«/mi»«mo»§#62;«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»dan«/mi»«mo»§#160;«/mo»«msup»«mn»0«/mn»«mo»§#176;«/mo»«/msup»«mo»§#8804;«/mo»«mi»x«/mi»«mo»§#8804;«/mo»«mn»360«/mn»«mo»§#176;«/mo»«/math»" role="math" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUwAAAAkCAYAAADivgPcAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAATRJrTQAAABylJREFUeNrtnX9kXlcYx4+IqKpSW6RVkYmKiZpS09ZEV/pHvSJiM9lkVbWZmaqZksXMVlOr/ZE/suo/M1OVjamIqG3MRMTMLCK6msh0FRVVpZ2IqAjvnsf7XLk5Oefcc+4979tk7/fDI/d9749zzvPe+73Pee65J0qBrUQ32RTZqvy9SrbLc99XyEbgQgBAvXCT7DhZg3x+i+yG574XyQbgQgBAvcLCueK5LQtrL1wGAKhX2sjuWNb1kM2QLZKdk+32w2UAgHpl3BI1nif7RlXym7vJhsmewF0AgHqEhXBEokidZrIFtZ7nZI6RTcBtIID3yJbJlmQZgG1JC9l3ZAcs618ju65994ZEnAD4wkLZStYuy6AGDJJ9FLj9INxmZQ/ZqPy10Ud2RftujOwduA8EsCw35TYIZm3okUgoFFtXE1RylgcztuGT/DfptreIPx+QleA+ENglXxLDzdbuoyhpi0ZVeSr7TI59eZ95sib8HpsoW0znlKrkMe+SnSZ7SLYD7tuAayD/JNlLOY7J+/DIBH6xYJasK+dvXAti1NXECbIvqlx3VxkcbE1Lu3jI3U9kL1p0ZkhVRpGsSpBRCvRRtLQFD6geLrD/sBwDgGrhGsjPD8l+CRROvmjmyA7L58Ny42/fgoIZq656z2ZcrKNK9fYpg9NPR1TloScHbucleEjDva+JlADytidFXEN8FC1twYOkuwvs363832ABIO85mjWQPy2cxzK2vWK4yZ9Vm/PJW0EwY9WV2S3R3i0RnWpQpIxG6WGl+cSjC+3jI05V/GtKW4ymwtUGUexSqjH3tC7fA2V+x3lMO/H44cXPZPu07XYaGpnVLS3XsDsDth9FBvInwjnhEE4+XrOh27fg0RvjfW+rygiHsqHev0u3kK+zfsP10CHX0YqkYbLy1XnrqsOi85f4s8FzH18NKFJGolMvkH1tCN5mPH77Qj7iISl9snxGVQZBJ58HpHuTZs1ynP2SX+DGNMld3jY8ZhXXOIhErIH8Hzhuyms5zmMWgREJNlg4LhuOz+s7ZblLIhpdMG9LtNwg3dHFjHasRbjmSiIebYE+DNGAvGUkwdM9y74rcuxZWf5exDWajwZT+Z5pWR6QRs+rzQ931hzHSvblE/iQY7vYglmG/W8shBgD+ZPtXRGm7Zx3CTPnyFoDu+Rlw+cDgcfIU1db9Denwp8Q+2pAkTIa5Le6ITcRvf2jaj0Puk8i395YPuqT0LZHosle+cxPYIcM29+XO7mJdqnMcUd5u6Rbjy45KEqRgfyJUE6p7BzmvKEL16zs7/rbggL9HOYI6ZrkydYsgqk8vitaV5/84gnPfXw0oGgZ6XbNa9+xtjRq3+2RdEYUH5VEqSel8ofk87Ql5LU99OECfxUBvugoDw99QCzyDORPC6XvcBsu46z2HX++6thnRgssWg1ix93tC6qS11eRBDNPXbPgaG1cfNueIWA+GlCkDD3SXNa+u2bQrZ2iZ1F8xCH/w1QDOffwSKJME6ZhRRw1cnI3GXj9lTKPj7JVFgAT1zNurnkG8ocIZTpqmkt1MY9INOK6sM/IdcIXdacIqC52y5Jfa5BAoiztKCKYeerqCz/FvuToOfpqQN4ybqa64ElkqmtRp/zGSW44OS9OxvJRo/xw6bshdxGet2zfpDbmNpukIekxbbyOn/7pA6pbpKIYuA58WFTZY+BqNZCfRXZWutoznqLbL3W7I/UsG9Y/EuPXjIe0dFUewcxb1yKEaEARuiVSXJNz45Kh+61EqLkXwQ99RpU5l1pTH+HVSFArbsEFNYfF/YnFxrZRGVuK0Mk0PlZP998o7JJQvdpPbkE8LkjXFgBQY15XmDcSAAC8+JHsTbgBAADc7CV7TPYsXAEAAG7eVeaHVL7TRYWyFfKeyL0CAHLxhzIPtveZLmq7AsEEAATznHTHGz22NU0XBcEEANQNn5F9mbGNa7ooGzyrN8+Y4vMOcJ5pupIIOGS6rDyCyW/L8IwuPFPOOW1dv7TRNPVYlg9itwcAUAP+JHs5Q1hc00XZWHJsbxLM0Gm6mJDpsvKMJ+V87biUw+NU0+9l81sb/GriDimbl7sCfFC0PQCAKvKpiEJ67rujZH97dMdd00XZ4Fc8B5T51a8Y03QlhEyXFXr8aYdgTWmRH7/WOhngg9jtAQBE5luyf1KfuSv+ecD+pumibPC79jwzC093d8pDMPN2mUOnywo5/mrgutUAH8RuDwCgCnCO8H1Zvq/sk4jYIs3lwPJKUk41BLPIdFk+x3f9c6wJtXHmHFOE6fJB7PYAAKrA2yKar6rKcCIXPtNFZXGwSoJZdLosH8FkoftBut6cU7ycWpfkMJuky23KYbp8ELs9AIAqMSeC8WHGdr7TRdkEiW2hCl3yWk2XxXRIWSx4p7V1/eKXu2r9/zz5+uBptQcAkEME+ELeC1cAAEA2R+ECAEAs/gOgm6s4rJ/s4gAAAfp0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+dzwvbWk+PG1mZW5jZWQ+PG1pPng8L21pPjwvbWZlbmNlZD48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtbj4yPC9tbj48bWk+ZDwvbWk+PC9tcm93Pjxtcm93Pjxtc3FydD48bW4+MzwvbW4+PC9tc3FydD48bW8+JiN4QTA7PC9tbz48bWk+c2luPC9taT48bW8+JiN4QTA7PC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtaT5jb3M8L21pPjxtbz4mI3hBMDs8L21vPjxtaT54PC9taT48L21yb3c+PC9tZnJhYz48bW8+LDwvbW8+PG1vPiYjeEEwOzwvbW8+PG1pPmQ8L21pPjxtbz4mZ3Q7PC9tbz48bW4+MDwvbW4+PG1vPiYjeEEwOzwvbW8+PG1pPmRhbjwvbWk+PG1vPiYjeEEwOzwvbW8+PG1zdXA+PG1uPjA8L21uPjxtbz4mI3hCMDs8L21vPjwvbXN1cD48bW8+JiN4MjI2NDs8L21vPjxtaT54PC9taT48bW8+JiN4MjI2NDs8L21vPjxtbj4zNjA8L21uPjxtbz4mI3hCMDs8L21vPjwvbWF0aD6bnZEtAAAAAElFTkSuQmCC" style="max-width: none;"> Tinjauan : 3 ​ sin x + cos x a cos x + b sin x cos x + 3 ​ sin x + R R α w ( x ) 6 0 ∘ + 9 0 ∘ ​ = = = = = = = ​ R cos ( x − α ) R cos ( x − α ) a 2 + b 2 ​ 1 2 + ( 3 ​ ) 2 ​ = 1 + 3 ​ = 4 ​ = 2 tan − 1 ( a b ​ ) = tan − 1 ( 1 3 ​ ​ ) = 6 0 ∘ 3 ​ s i n x + c o s x 2 d ​ = 2 c o s ( x − 60 ) ∘ 2 d ​ = c o s ( x − 60 ) ∘ d ​ 15 0 ∘ ∈ [ 0 ∘ , 36 0 ∘ ] ​ Berdasarkan konsep limit kanan dan limit kiri di atas maka : Dengan demikian, w ( x ) tidak memiliki nilai minimum dan maksimum.