{"id":8076,"date":"2021-11-13T21:12:09","date_gmt":"2021-11-13T15:42:09","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8076"},"modified":"2021-11-14T00:57:11","modified_gmt":"2021-11-13T19:27:11","slug":"find-the-equation-of-the-normal-to-the-curve-y-2x2-3-sin-x-at-x-0","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-equation-of-the-normal-to-the-curve-y-2x2-3-sin-x-at-x-0\/","title":{"rendered":"Find the equation of the normal to the curve y = \\(2x^2 + 3 sin x\\) at x = 0."},"content":{"rendered":"

Solution :<\/h2>\n

The equation of the given curve is<\/p>\n

y = \\(2x^2 + 3 sin x\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0……….(i)<\/p>\n

Putting x = 0 in (i), we get y = 0.<\/p>\n

So, the point of contact is (0, 0).<\/p>\n

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

Differentiating with respect to x,<\/p>\n

\\(\\implies\\)\u00a0 \\(dy\\over dx\\)\u00a0 = 4x + 3 cos x<\/p>\n

\\(\\implies\\)\u00a0 \\(({dy\\over dx})_{(0, 0)}\\) = 4 \\(\\times\\) 0 + 3 cos 0 = 3<\/p>\n

So, the equation of the normal<\/a> at (0, 0) is<\/p>\n

y – 0 = -\\(1\\over 3\\)(x – 0)\u00a0 or,\u00a0 x + 3y = 0<\/p>\n

\n

Similar Questions<\/h3>\n

Find the equations of the tangent and the normal at the point \u2018t\u2019 on the curve x = \\(a sin^3 t\\), y = \\(b cos^3 t\\).<\/a><\/p>\n

Find the equation of the tangent to curve y = \\(-5x^2 + 6x + 7\\)\u00a0 at the point (1\/2, 35\/4).<\/a><\/p>\n

Find the angle between the curves xy = 6 and \\(x^2 y\\) =12.<\/a><\/p>\n

Check the orthogonality of the curves \\(y^2\\) = x and \\(x^2\\) = y.<\/a><\/p>\n

The angle of intersection between the curve \\(x^2\\) = 32y and \\(y^2\\) = 4x at point (16, 8) is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : The equation of the given curve is y = \\(2x^2 + 3 sin x\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0……….(i) Putting x = 0 in (i), we get y = 0. So, the point of contact is (0, 0). Now, y = \\(2x^2 + 3 sin x\\) Differentiating with respect …<\/p>\n

Find the equation of the normal to the curve y = \\(2x^2 + 3 sin x\\) at x = 0.<\/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 equation of the normal to the curve y = \\(2x^2 + 3 sin x\\) at x = 0.<\/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-equation-of-the-normal-to-the-curve-y-2x2-3-sin-x-at-x-0\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the equation of the normal to the curve y = \\(2x^2 + 3 sin x\\) at x = 0.\" \/>\n<meta property=\"og:description\" content=\"Solution : The equation of the given curve is y = (2x^2 + 3 sin x)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0……….(i) Putting x = 0 in (i), we get y = 0. 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