{"id":8161,"date":"2021-11-15T00:07:37","date_gmt":"2021-11-14T18:37:37","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8161"},"modified":"2021-11-15T16:04:06","modified_gmt":"2021-11-15T10:34:06","slug":"find-the-approximate-value-of-f3-02-where-fx-3x2-5x-3","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-approximate-value-of-f3-02-where-fx-3x2-5x-3\/","title":{"rendered":"Find the approximate value of f(3.02), where f(x) = \\(3x^2 + 5x + 3\\)."},"content":{"rendered":"

Solution :<\/h2>\n

Let y = f(x), x = 3 and x + \\(\\delta x\\). Then, \\(\\delta x\\).= 0.02.<\/p>\n

For x = 3, we get<\/p>\n

y = f(3) = 45<\/p>\n

Now, y = f(x) \\(\\implies\\) y = \\(3x^2 + 5x + 3\\)<\/p>\n

\\(\\implies\\) \\(dy\\over dx\\) = 6x + 5 \\(\\implies\\)\u00a0 \\(({dy\\over dx})_{x = 3}\\) = 23<\/p>\n

Let \\(\\delta y\\) be the change in y due to change \\(\\delta x\\) in x. Then,<\/p>\n

\\(\\delta y\\) = \\(dy\\over dx\\) \\(\\delta x\\)\u00a0 \\(\\implies\\)\u00a0 \\(\\delta y\\) = \\(23 \\times 0.02\\) = 0.46<\/p>\n

f(3.02) = y + \\(\\delta y\\) = 45 + 0.46 = 45.46<\/p>\n

\n

Similar Questions<\/h3>\n

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.<\/a><\/p>\n

Verify Rolle\u2019s theorem for the function f(x) = \\(x^2\\) \u2013 5x + 6 on the interval [2, 3].<\/a><\/p>\n

It is given that for the function f(x) = \\(x^3 \u2013 6x^2 + ax + b\\) on [1, 3], Rolles\u2019s theorem holds with c = \\(2 +{1\\over \\sqrt{3}}\\). Find the values of a and b, if f(1) = f(3) = 0.<\/a><\/p>\n

Find the point on the curve y = cos x \u2013 1, x \\(\\in\\) \\([{\\pi\\over 2}, {3\\pi\\over 2}]\\) at which tangent is parallel to the x-axis.<\/a><\/p>\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let y = f(x), x = 3 and x + \\(\\delta x\\). Then, \\(\\delta x\\).= 0.02. For x = 3, we get y = f(3) = 45 Now, y = f(x) \\(\\implies\\) y = \\(3x^2 + 5x + 3\\) \\(\\implies\\) \\(dy\\over dx\\) = 6x + 5 \\(\\implies\\)\u00a0 \\(({dy\\over dx})_{x = 3}\\) = 23 …<\/p>\n

Find the approximate value of f(3.02), where f(x) = \\(3x^2 + 5x + 3\\).<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[66,43],"tags":[],"yoast_head":"\nFind the approximate value of f(3.02), where f(x) = \\(3x^2 + 5x + 3\\).<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/find-the-approximate-value-of-f3-02-where-fx-3x2-5x-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the approximate value of f(3.02), where f(x) = \\(3x^2 + 5x + 3\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : Let y = f(x), x = 3 and x + (delta x). Then, (delta x).= 0.02. For x = 3, we get y = f(3) = 45 Now, y = f(x) (implies) y = (3x^2 + 5x + 3) (implies) (dyover dx) = 6x + 5 (implies)\u00a0 (({dyover dx})_{x = 3}) = 23 … Find the approximate value of f(3.02), where f(x) = (3x^2 + 5x + 3). 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